Mensuration for JKSSB Class IV

Mensuration is one of those mathematics topics that looks formula-based at first, but becomes much easier once you understand what the question is actually asking.

A question may mention a field, room, floor, wall, garden, boundary, tank, box, square, rectangle, circle or rectangular plot, and your job is to identify what quantity is required:

Perimeter → boundary or distance around a figure
Area → surface covered by a two-dimensional figure
Volume → space occupied by a three-dimensional object
Capacity → amount a container can hold
Cost → quantity × rate

Read: JKPSI Quantitative Aptitude Tests

This distinction is extremely important for competitive examinations. Many questions do not directly say “find the perimeter” or “find the area.” Instead, they use everyday language such as:

A man walks around a rectangular field.

That means perimeter.

A farmer wants to fence a rectangular field.

That also means perimeter.

A room is to be tiled.

That normally means area of the floor.

A wall is to be painted.

That means area of the wall.

A water tank is 2 m long, 1.5 m wide and 1 m high.

That means volume/capacity.

So, before memorising formulas, learn to identify the mathematical quantity hidden inside the language of the question.

For JKSSB preparation, this is especially useful because objective questions often test whether the candidate can select the correct formula quickly rather than merely perform a long calculation.

1. What Is Mensuration?

Mensuration is the branch of mathematics concerned with the measurement of geometric quantities such as:

length
perimeter
area
volume
surface area
capacity

In simple words:

Mensuration tells us how much boundary, surface or space a geometrical object has.

There are two broad categories.

Type	Meaning	Examples
2D figures	Flat figures having length and breadth	Square, rectangle, triangle, circle
3D figures	Solid objects having length, breadth and height/depth	Cube, cuboid, cylinder

This distinction is fundamental.

A rectangle drawn on paper is a 2D figure.

A rectangular box is a 3D object.

The rectangle has:

length
breadth

The cuboid has:

length
breadth
height

Therefore:

Rectangle → area

Cuboid → volume

That simple distinction solves many basic mensuration questions.

2. Why Mensuration Matters in JKSSB Exams

Mensuration is not only about memorising formulas. It tests several mathematical skills at once:

understanding the question,
recognising the correct figure,
selecting the correct formula,
maintaining correct units,
performing arithmetic accurately.

A question can therefore look simple but still contain a trap.

For example:

Question

A rectangular field is 25 m long and 15 m broad. Find the cost of fencing it at ₹8 per metre.

A student who calculates:

[
25 \times 15 = 375
]

has found the area, not the quantity required for fencing.

The correct quantity is the perimeter:

[
2(l+b)
]

[
=2(25+15)=80m
]

Cost:

[
80\times8=₹640
]

This is an excellent example of why concept first, formula second is the correct approach.

3. The Three Most Important Questions in Mensuration

Whenever you see a mensuration problem, ask yourself:

Question 1: Am I measuring the boundary?

If yes → Perimeter

Question 2: Am I measuring the surface covered?

If yes → Area

Question 3: Am I measuring the space occupied?

If yes → Volume

A very useful memory line is:

Boundary = Perimeter
Surface = Area
Space = Volume

Remember these three words before remembering dozens of formulas.

4. Perimeter – The Boundary of a Figure

The perimeter is the total distance around a closed two-dimensional figure.

Imagine walking around the boundary of a rectangular field. The total distance covered by you is the perimeter of the field.

Similarly:

fencing a field → perimeter
putting a wire around a garden → perimeter
walking around a park → perimeter
framing a rectangular photo → perimeter

Important idea

Perimeter is a measurement of length, so its units are ordinary length units:

It is not measured in square units.

This is a common exam trap.

Quantity	Unit
Length	cm, m, km
Perimeter	cm, m, km
Area	cm², m², km²
Volume	cm³, m³
Capacity	L, mL

5. Rectangle

A rectangle is a four-sided figure in which:

opposite sides are equal
all four angles are right angles

For a rectangle:

Length = (l)
Breadth = (b)

Perimeter of Rectangle

[
P=2(l+b)
]

Why?

A rectangle has two lengths and two breadths:

[
P=l+b+l+b
]

Therefore:

[
P=2l+2b
]

[
\boxed{P=2(l+b)}
]

Example

Length = 14 cm
Breadth = 9 cm

[
P=2(14+9)
]

[
=2\times23
]

[
=46cm
]

Answer:

46 cm

6. Area of a Rectangle

Area means the amount of surface occupied by the rectangle.

The formula is:

[
\boxed{A=l\times b}
]

Example

Length = 16 m
Breadth = 7 m

[
A=16\times7
]

[
A=112m^2
]

Notice the unit.

The dimensions are measured in metres, but area is measured in square metres.

This is not a decoration. The square in (m^2) tells us that we are measuring a two-dimensional surface.

7. Perimeter vs Area of Rectangle

This distinction is among the most important things to master.

Property	Perimeter	Area
Meaning	Boundary	Surface
Formula	(2(l+b))	(l\times b)
Unit	m, cm, km	m², cm², km²
Used for	fencing, boundary	flooring, painting surface
Nature	one-dimensional measurement	two-dimensional measurement

Example

A field is 20 m × 10 m.

Perimeter:

[
2(20+10)=60m
]

Area:

[
20\times10=200m^2
]

The answers are not interchangeable.

8. Square

A square is a special rectangle.

It has:

four equal sides
four right angles

If each side is (a):

Perimeter of Square

[
\boxed{P=4a}
]

Area of Square

[
\boxed{A=a^2}
]

Example

Side = 12 cm

Perimeter:

[
4\times12=48cm
]

Area:

[
12^2=144cm^2
]

9. An Important Relationship Between Square and Rectangle

Every square is a rectangle, but every rectangle is not a square.

Why?

Because a rectangle has opposite sides equal, while a square has all four sides equal.

This distinction frequently appears in reasoning-type questions as well as mathematics questions.

Feature	Rectangle	Square
Number of sides	4	4
Opposite sides	Equal	Equal
All sides equal	Not necessarily	Yes
All angles	90°	90°
Perimeter	(2(l+b))	(4a)
Area	(lb)	(a^2)

10. Finding the Side of a Square from Its Perimeter

Suppose a square has perimeter 64 cm.

We know:

[
P=4a
]

Therefore:

[
a=\frac{P}{4}
]

[
a=\frac{64}{4}=16cm
]

Shortcut

For a square:

Side = Perimeter ÷ 4

11. Finding the Side of a Square from Its Area

Suppose area = 225 cm².

Since:

[
A=a^2
]

we take square root:

[
a=\sqrt{225}
]

[
a=15cm
]

Important Square Roots to Remember

Number	Square
1	1
2	4
3	9
4	16
5	25
6	36
7	49
8	64
9	81
10	100
11	121
12	144
13	169
14	196
15	225
16	256
17	289
18	324
19	361
20	400

These values are highly useful for speed calculations.

12. Triangle

A triangle is a closed figure with:

three sides
three angles

Triangles are important because many students remember the area formula but forget the meaning of the height.

Area of Triangle

[
\boxed{A=\frac12 bh}
]

where:

(b) = base
(h) = perpendicular height

Example

Base = 12 cm
Height = 8 cm

[
A=\frac12\times12\times8
]

[
A=48cm^2
]

13. Why Is There a Half in the Triangle Formula?

This is not a random formula.

Imagine a rectangle.

A diagonal line drawn from one corner to the opposite corner divides the rectangle into two equal triangles.

Therefore, each triangle occupies half the area of the rectangle.

Rectangle area:

[
b\times h
]

Triangle area:

[
\frac12\times b\times h
]

So:

[
\boxed{\text{Triangle area}=\frac12 bh}
]

This conceptual understanding makes the formula much easier to remember.

14. Common Triangle Mistake

Students sometimes use a slanting side as the height.

That is not necessarily correct.

The height must be perpendicular to the base.

Therefore:

Base and perpendicular height are the pair used in the triangle area formula.

In an objective question, a diagram may deliberately provide several lengths. Do not automatically use the longest side.

15. Parallelogram

A parallelogram has:

opposite sides parallel
opposite sides equal

Its area is:

[
\boxed{A=bh}
]

where:

(b) = base
(h) = perpendicular height

Example

Base = 18 cm
Height = 7 cm

[
A=18\times7
]

[
=126cm^2
]

Important comparison

Triangle:

[
\frac12 bh
]

Parallelogram:

[
bh
]

Therefore, for the same base and height, a triangle has half the area of a parallelogram.

16. Rhombus

A rhombus is a four-sided figure in which all sides are equal.

Its area can be calculated using its diagonals:

[
\boxed{A=\frac12 d_1d_2}
]

where:

(d_1) = first diagonal
(d_2) = second diagonal

Example

Diagonal 1 = 10 cm
Diagonal 2 = 16 cm

[
A=\frac12\times10\times16
]

[
=80cm^2
]

Perimeter:

[
\boxed{4a}
]

because all four sides have equal length.

17. Trapezium

A trapezium has one pair of parallel sides.

If parallel sides are (a) and (b), and height is (h):

[
\boxed{A=\frac12(a+b)h}
]

Example

Parallel sides = 12 cm and 18 cm
Height = 6 cm

[
A=\frac12(12+18)\times6
]

[
=\frac12\times30\times6
]

[
=90cm^2
]

For basic JKSSB-level preparation, understand the structure of the formula rather than trying to memorise it without meaning.

18. Circle

A circle is a round figure in which every point on the boundary is at the same distance from the centre.

Important terms:

Centre
Radius
Diameter
Circumference

Radius

The distance from the centre to the boundary.

Represented by:

[
r
]

Diameter

A straight line passing through the centre and joining two points on the circle.

[
\boxed{d=2r}
]

Therefore:

[
\boxed{r=\frac d2}
]

This relationship should be memorised.

19. Circumference of a Circle

The boundary length of a circle is called its circumference.

Formula:

[
\boxed{C=2\pi r}
]

[
\boxed{C=\pi d}
]

Both forms are correct.

For many school-level competitive questions:

[
\pi=\frac{22}{7}
]

or sometimes:

[
\pi=3.14
]

Use the value specified in the question. If none is given and the numbers suggest 22/7, that value is often intended.

20. Area of a Circle

The area of a circle is:

[
\boxed{A=\pi r^2}
]

The radius is squared.

That means:

[
A=\pi\times r\times r
]

Example

Radius = 7 cm

Using:

[
\pi=\frac{22}{7}
]

[
A=\frac{22}{7}\times7\times7
]

[
=154cm^2
]

21. Circumference vs Area of Circle

Quantity	Formula	Unit
Circumference	(2\pi r)	cm, m
Area	(\pi r^2)	cm², m²

This is another common objective-question trap.

A boundary question involving a circular track usually points toward circumference.

A question asking how much land is covered by the circle points toward area.

22. Semicircle

A semicircle is half of a circle.

Area

[
\boxed{A=\frac12\pi r^2}
]

However, the perimeter requires special care.

The boundary of a semicircle consists of:

the curved half of the circle
the diameter

Therefore:

[
\boxed{\text{Perimeter of semicircle}=\pi r+2r}
]

A common mistake is to write only (\pi r).

That is only the curved portion, not the complete boundary.

23. Quarter Circle

A quarter circle is one-fourth of a circle.

Area:

[
\boxed{A=\frac14\pi r^2}
]

The complete boundary depends on what exactly the question asks, because a quarter-circle boundary contains:

one-fourth of the circumference
two radii

Therefore the perimeter is:

[
\boxed{\frac{\pi r}{2}+2r}
]

This is more useful for advanced practice than for routine basic questions, but understanding the logic prevents mistakes.

24. Circumference and Diameter: A Useful Relationship

Since:

[
d=2r
]

and

[
C=2\pi r
]

we can write:

[
C=\pi d
]

This is especially convenient if the question gives the diameter directly.

Example

Diameter = 14 cm.

[
C=\pi d
]

[
=\frac{22}{7}\times14
]

[
=44cm
]

There was no need to first find the radius.

25. Units of Measurement

Unit conversion is one of the most neglected parts of mensuration.

Suppose:

Length = 2 m
Breadth = 50 cm

You cannot directly multiply:

[
2\times50
]

until the units are made the same.

Convert:

[
2m=200cm
]

Then:

[
Area=200\times50=10000cm^2
]

Or convert 50 cm into metres:

[
50cm=0.5m
]

Then:

[
Area=2\times0.5=1m^2
]

Both answers represent the same physical area.

26. Important Length Conversions

Conversion	Value
1 cm	10 mm
1 m	100 cm
1 m	1000 mm
1 km	1000 m
1 km	100,000 cm

The most important chain is:

[
1km=1000m=100000cm
]

27. Important Area Conversions

This is where many candidates make mistakes.

Because area involves two dimensions, the conversion factor is squared.

Since:

[
1m=100cm
]

therefore:

[
1m^2=100\times100cm^2
]

So:

[
\boxed{1m^2=10000cm^2}
]

Similarly:

[
1km^2=(1000m)^2
]

[
=1,000,000m^2
]

Thus:

[
\boxed{1km^2=10^6m^2}
]

28. Important Volume Conversions

Because volume has three dimensions:

[
1m=100cm
]

Therefore:

[
1m^3=100\times100\times100cm^3
]

[
\boxed{1m^3=1,000,000cm^3}
]

This “power rule” is useful:

length → factor 100
area → factor (100^2)
volume → factor (100^3)

29. Quick Unit Revision Table

Quantity	Basic Conversion
1 m	100 cm
1 m²	10,000 cm²
1 m³	10,00,000 cm³
1 km	1000 m
1 km²	10,00,000 m²
1 litre	1000 mL
1 m³	1000 litres
1 litre	1000 cm³
1 hectare	10,000 m²

Very Important

Do not write:

[
1m^2=100cm^2
]

That is wrong.

Correct:

[
1m^2=10000cm^2
]

30. Hectare and Square Metre

Agricultural-land questions may use hectare.

[
\boxed{1 hectare=10,000m^2}
]

Therefore:

[
2ha=20,000m^2
]

and:

[
0.5ha=5,000m^2
]

A hectare is a unit of area, not length.

31. Three-Dimensional Figures

Now we move from measuring flat surfaces to measuring solid objects.

A three-dimensional object has depth as well as length and breadth.

Common solids:

cube
cuboid
cylinder

For the basic level, cube and cuboid deserve special attention.

32. Cuboid

A cuboid is a box-like solid.

Examples:

brick
rectangular box
room
cupboard
water tank

Its dimensions are:

length (l)
breadth (b)
height (h)

33. Volume of Cuboid

Volume means the amount of space occupied by the solid.

Formula:

[
\boxed{V=lbh}
]

Example

Length = 10 cm
Breadth = 6 cm
Height = 4 cm

[
V=10\times6\times4
]

[
=240cm^3
]

Notice that the unit is cubic centimetres.

34. Why Is Cuboid Volume (lbh)?

Imagine a cuboid as a stack of identical rectangular layers.

One layer has:

[
l\times b
]

area.

If there are (h) units of height:

[
Volume=Area\ of\ base\times Height
]

Therefore:

[
V=lbh
]

This relationship is important enough to remember:

Volume = Base Area × Height

For a cuboid:

[
Base\ Area=l\times b
]

so:

[
V=lbh
]

35. Capacity of a Cuboidal Tank

Suppose a water tank measures:

2 m × 1.5 m × 1 m

Volume:

[
2\times1.5\times1=3m^3
]

Since:

[
1m^3=1000L
]

therefore:

[
3m^3=3000L
]

Answer:

3000 litres

This type of question combines:

volume
multiplication
unit conversion

and is a useful competitive-exam pattern.

36. Surface Area of a Cuboid

A cuboid has six rectangular faces.

The total surface area is:

[
\boxed{TSA=2(lb+bh+hl)}
]

Why?

The six faces occur in three pairs:

top and bottom → (lb)
front and back → (lh)
left and right → (bh)

Thus:

[
2lb+2lh+2bh
]

or:

[
2(lb+bh+hl)
]

37. Lateral Surface Area of a Cuboid

The lateral surface area excludes the top and bottom.

Therefore:

[
\boxed{LSA=2h(l+b)}
]

This represents the four vertical faces.

Such questions can become slightly more advanced, so read the wording carefully.

If the question says:

Find the area of the four walls of a room.

You generally need the lateral surface area, not the total surface area.

38. Cube

A cube is a special cuboid in which:

length = breadth = height
all six faces are squares
all edges are equal

If edge = (a):

Volume

[
\boxed{V=a^3}
]

Total Surface Area

[
\boxed{TSA=6a^2}
]

Lateral Surface Area

[
\boxed{LSA=4a^2}
]

Perimeter of one face

Since one face is a square:

[
4a
]

39. Cube Example

Edge = 5 cm

Volume:

[
5^3=125cm^3
]

TSA:

[
6(5^2)
]

[
=6\times25
]

[
=150cm^2
]

LSA:

[
4(5^2)
]

[
=100cm^2
]

40. Formula Master Table

This table is worth saving for revision.

Figure	Quantity	Formula
Rectangle	Perimeter	(2(l+b))
Rectangle	Area	(lb)
Square	Perimeter	(4a)
Square	Area	(a^2)
Triangle	Area	(\frac12bh)
Parallelogram	Area	(bh)
Rhombus	Area	(\frac12d_1d_2)
Trapezium	Area	(\frac12(a+b)h)
Circle	Circumference	(2\pi r)
Circle	Area	(\pi r^2)
Semicircle	Area	(\frac12\pi r^2)
Cuboid	Volume	(lbh)
Cuboid	TSA	(2(lb+bh+hl))
Cuboid	LSA	(2h(l+b))
Cube	Volume	(a^3)
Cube	TSA	(6a^2)
Cube	LSA	(4a^2)

41. The Most Important Language Clues in Mensuration

Examiners often hide the mathematical operation inside ordinary language.

Wording in Question	Usually Means
Around a field	Perimeter
Fence a field	Perimeter
Boundary of a garden	Perimeter
Walking around a park	Perimeter
Flooring a room	Area
Tiling a floor	Area
Painting a wall	Area
Carpet required	Area
Land covered	Area
Space occupied	Volume
Water a tank can hold	Volume/Capacity
Capacity of container	Volume/Capacity
Four walls of room	Lateral surface area

Teacher's Tip

Do not rush into calculation.

First underline the word that tells you what is being measured.

42. Cost-Based Mensuration Questions

Many exam problems combine measurement with money.

The general idea is:

[
\boxed{Cost=Quantity\times Rate}
]

The difficult part is identifying the correct quantity.

Fencing

[
Cost=Perimeter\times Rate
]

Flooring

[
Cost=Area\times Rate
]

Painting

[
Cost=Area\times Rate
]

Filling a tank

You may need volume/capacity first.

43. Example: Cost of Fencing

A rectangular field is 30 m long and 20 m wide. Find the cost of fencing it at ₹15 per metre.

First find perimeter:

[
P=2(30+20)
]

[
=100m
]

Now cost:

[
100\times15=₹1500
]

Answer

₹1500

44. Example: Cost of Flooring

A room is 8 m long and 6 m wide. Flooring costs ₹120 per square metre.

Area:

[
8\times6=48m^2
]

Cost:

[
48\times120
]

[
=₹5760
]

The common mistake would be calculating the perimeter.

Remember:

Flooring covers the surface, therefore use area.

45. Example: Painting a Wall

A wall is 10 m long and 4 m high. Find the area to be painted.

[
A=10\times4
]

[
=40m^2
]

If painting costs ₹25 per square metre:

[
40\times25=₹1000
]

If the question says there are doors/windows and asks for the paintable area, subtract their areas from the total wall area.

46. Composite Figures

A composite figure is a shape made of two or more simple figures.

For example, an irregular shape may be formed by:

a rectangle + rectangle
rectangle + square
rectangle + semicircle

Do not become frightened when the shape looks unfamiliar.

The best approach is:

Step 1

Break the figure into familiar shapes.

Step 2

Find the area of each part.

Step 3

Add the areas if the parts are joined.

Step 4

Subtract areas when there is a cut-out.

A useful mental rule:

Unknown shape = known shapes combined.

47. Example of Composite Area

Suppose a shape can be divided into:

Rectangle 1: 10 × 5
Rectangle 2: 4 × 3

Area of rectangle 1:

[
10\times5=50
]

Area of rectangle 2:

[
4\times3=12
]

Total:

[
50+12=62
]

So the composite area is:

[
\boxed{62\text{ square units}}
]

The important lesson is not the arithmetic. It is the decomposition of the shape.

48. Finding Missing Dimensions

Mensuration questions often give area or perimeter and ask for a missing side.

Suppose a rectangle has area 180 cm² and length 15 cm.

Using:

[
A=lb
]

we have:

[
180=15b
]

Therefore:

[
b=\frac{180}{15}
]

[
b=12cm
]

Formula Rearrangement

For rectangle:

[
A=lb
]

therefore:

[
l=\frac Ab
]

and

[
b=\frac Al
]

Understanding rearrangement saves time.

49. Rectangle from Perimeter

Suppose:

Perimeter = 50 cm
Length = 15 cm

Formula:

[
P=2(l+b)
]

Substitute:

[
50=2(15+b)
]

Divide by 2:

[
25=15+b
]

Therefore:

[
b=10cm
]

This kind of question tests algebraic understanding along with mensuration.

50. If Perimeter Is Fixed, Area Can Change

This is a useful conceptual observation.

Take a rectangle with perimeter 40 cm.

Case 1

Length = 15 cm
Breadth = 5 cm

Area:

[
15\times5=75cm^2
]

Case 2

Length = 12 cm
Breadth = 8 cm

Area:

[
12\times8=96cm^2
]

Both have perimeter:

[
2(15+5)=40
]

and:

[
2(12+8)=40
]

But their areas are different.

This teaches an important point:

Same perimeter does not necessarily mean same area.

In contrast, among rectangles with the same perimeter, the square has the greatest area.

For basic competitive exams, this is a useful conceptual fact.

51. Same Area Does Not Necessarily Mean Same Perimeter

Consider:

Rectangle A

10 × 6

Area:

[
60
]

Perimeter:

[
32
]

Rectangle B

12 × 5

Area:

[
60
]

Perimeter:

[
34
]

Both have the same area but different perimeters.

This is another common conceptual trap.

52. Square vs Rectangle – Important Concept

If a square and a rectangle have equal perimeter, their areas need not be equal.

If a square and rectangle have equal area, their perimeters need not be equal.

Therefore:

Area and perimeter measure different properties and cannot be treated as interchangeable.

53. Ratio-Based Mensuration

Mensuration may also be tested through ratios.

Suppose the sides of two squares are in the ratio:

[
2:3
]

Their areas are in the ratio:

[
2^2:3^2
]

[
=4:9
]

This gives a very important general principle:

When linear dimensions are in ratio (a), corresponding areas are often in ratio (a^2^2).

Similarly, corresponding volumes are in ratio:

[
a^3^3
]

This is more advanced but useful for difficult objective questions.

54. Scaling Rule

If the side of a square is doubled:

Original area:

[
a^2
]

New side:

[
2a
]

New area:

[
(2a)^2=4a^2
]

So doubling the side makes the area four times, not two times.

Similarly:

If all three dimensions of a cuboid are doubled:

[
(2l)(2b)(2h)=8lbh
]

Therefore its volume becomes 8 times.

Memory Rule

Dimension Change	Effect on Area	Effect on Volume
Double	4×	8×
Triple	9×	27×
Half	1/4×	1/8×

55. A Very Common Trap: Radius vs Diameter

Suppose diameter is 14 cm.

Some students directly use 14 in:

[
A=\pi r^2
]

This is wrong because the formula requires radius.

First:

[
r=\frac{14}{2}=7cm
]

Then:

[
A=\frac{22}{7}\times7^2
]

[
=154cm^2
]

Memory Line

Diameter is double the radius.

Never put the diameter directly into (πr^2).

56. Another Common Trap: Squaring the Entire Expression

Suppose:

[
r=7
]

Area:

[
\pi r^2
]

This means:

[
\pi\times7^2
]

not:

[
(\pi\times7)^2
]

Keep the formula exactly as written.

57. Choosing (\pi)

Common values:

[
\pi=\frac{22}{7}
]

and

[
\pi=3.14
]

When the radius or diameter is a multiple of 7, (22/7) often makes the calculation easier.

Example:

[
r=14
]

[
A=\frac{22}{7}\times14\times14
]

Cancel 14 with 7:

[
=22\times2\times14
]

[
=616cm^2
]

The exact arithmetic depends on the question, but the strategic principle is:

Choose the permitted value of (\pi) that makes calculation convenient, unless the question specifies otherwise.

58. Area of Four Walls of a Room

Suppose a room has:

length = (l)
breadth = (b)
height = (h)

The area of the four walls is:

[
2h(l+b)
]

Why?

There are two walls of dimensions:

[
l\times h
]

and two walls of dimensions:

[
b\times h
]

Therefore:

[
2lh+2bh
]

[
=2h(l+b)
]

Important

If the question asks for four walls, do not include the floor and ceiling.

59. Flooring a Room

Floor area:

[
l\times b
]

You do not include height.

Example:

Room:

10 m × 8 m × 4 m

Floor area:

[
10\times8=80m^2
]

Four walls:

[
2(4)(10+8)=144m^2
]

The dimensions are the same room, but the required area depends on the wording.

60. Painting Four Walls

If a room is:

12 m long
8 m broad
4 m high

Area of four walls:

[
2h(l+b)
]

[
=2(4)(12+8)
]

[
=8\times20
]

[
=160m^2
]

If the room has doors and windows, subtract their combined area if the question asks for actual paintable area.

61. Open and Closed Boxes

A cuboid may have:

all six surfaces
top open
bottom open
one side open

This changes the required surface area.

For a completely closed cuboid:

[
TSA=2(lb+bh+hl)
]

But an open-top box excludes the top face.

Therefore the top-face area (lb) must be subtracted.

This is a useful concept for tougher practice.

62. Difference Between Area, Surface Area and Volume

Term	Meaning
Area	Surface occupied by a 2D figure
Surface Area	Total outer surface of a 3D object
Volume	Space inside/occupied by a 3D object

For example:

A rectangular room floor → area

A cube's six outer faces together → surface area

A water tank's internal space → volume/capacity

63. The “What Exactly Is Being Asked?” Method

Before solving any question, silently ask:

Step A – Identify the object

Is it:

square?
rectangle?
triangle?
circle?
cube?
cuboid?

Step B – Identify the quantity

Is the question asking for:

perimeter?
area?
circumference?
surface area?
volume?

Step C – Check units

Are all dimensions in the same unit?

Step D – Calculate

Only now use the formula.

This four-step process greatly reduces careless mistakes.

64. Solved Problem 1 – Rectangle Perimeter

A rectangular playground has length 32 m and breadth 18 m. Find its perimeter.

[
P=2(l+b)
]

[
=2(32+18)
]

[
=2(50)
]

[
=100m
]

Answer: 100 m

65. Solved Problem 2 – Rectangle Area

A rectangular field is 45 m long and 20 m wide.

[
A=l\times b
]

[
=45\times20
]

[
=900m^2
]

Answer: 900 m²

66. Solved Problem 3 – Square Perimeter

Side of square = 18 cm.

[
P=4a
]

[
=4\times18
]

[
=72cm
]

Answer: 72 cm

67. Solved Problem 4 – Square Area

Side = 16 m.

[
A=a^2
]

[
=16^2
]

[
=256m^2
]

Answer: 256 m²

68. Solved Problem 5 – Triangle Area

Base = 24 cm
Height = 15 cm

[
A=\frac12bh
]

[
=\frac12\times24\times15
]

[
=12\times15
]

[
=180cm^2
]

Answer: 180 cm²

69. Solved Problem 6 – Circle Circumference

Radius = 14 cm.

[
C=2\pi r
]

[
=2\times\frac{22}{7}\times14
]

[
=88cm
]

Answer: 88 cm

70. Solved Problem 7 – Circle Area

Radius = 14 cm.

[
A=\pi r^2
]

[
=\frac{22}{7}\times14\times14
]

[
=616cm^2
]

Answer: 616 cm²

71. Solved Problem 8 – Cuboid Volume

Length = 12 cm
Breadth = 8 cm
Height = 5 cm

[
V=lbh
]

[
=12\times8\times5
]

[
=480cm^3
]

Answer: 480 cm³

72. Solved Problem 9 – Cost of Fencing

Length = 25 m
Breadth = 16 m
Rate = ₹12 per metre

Perimeter:

[
2(25+16)=82m
]

Cost:

[
82\times12
]

[
=₹984
]

Answer: ₹984

73. Solved Problem 10 – Cost of Flooring

Length = 12 m
Breadth = 9 m
Rate = ₹50/m²

Area:

[
12\times9=108m^2
]

Cost:

[
108\times50
]

[
=₹5400
]

Answer: ₹5,400

74. Solved Problem 11 – Missing Breadth

Area = 360 m²
Length = 24 m

[
A=lb
]

Therefore:

[
b=\frac{A}{l}
]

[
=\frac{360}{24}
]

[
=15m
]

Answer: 15 m

75. Solved Problem 12 – Missing Side from Perimeter

Perimeter of square = 92 cm.

[
4a=92
]

[
a=23cm
]

Answer: 23 cm

76. Solved Problem 13 – Tank Capacity

A cuboidal tank measures 3 m × 2 m × 1.5 m.

Volume:

[
3\times2\times1.5=9m^3
]

Since:

[
1m^3=1000L
]

therefore:

[
9m^3=9000L
]

Answer: 9,000 litres

77. Solved Problem 14 – Unit Conversion

A rectangle is 2 m long and 75 cm wide. Find the area in square metres.

Convert 75 cm:

[
75cm=0.75m
]

Area:

[
2\times0.75=1.5m^2
]

Answer: 1.5 m²

78. Solved Problem 15 – Semicircle Area

Radius = 14 cm.

[
A=\frac12\pi r^2
]

[
=\frac12\times\frac{22}{7}\times14\times14
]

Full circle area:

[
616cm^2
]

Half:

[
308cm^2
]

Answer: 308 cm²

79. Solved Problem 16 – Semicircle Perimeter

Radius = 7 cm.

[
P=\pi r+2r
]

[
=\frac{22}{7}\times7+14
]

[
=22+14
]

[
=36cm
]

Answer: 36 cm

80. Solved Problem 17 – Painting Four Walls

A room is 8 m long, 6 m broad and 4 m high. Find the area of its four walls.

[
2h(l+b)
]

[
=2(4)(8+6)
]

[
=8\times14
]

[
=112m^2
]

Answer: 112 m²

81. Solved Problem 18 – Area of Rhombus

Diagonals are 18 cm and 12 cm.

[
A=\frac12d_1d_2
]

[
=\frac12\times18\times12
]

[
=108cm^2
]

Answer: 108 cm²

82. Solved Problem 19 – Trapezium

Parallel sides are 14 cm and 20 cm and height is 8 cm.

[
A=\frac12(a+b)h
]

[
=\frac12(14+20)\times8
]

[
=17\times8
]

[
=136cm^2
]

Answer: 136 cm²

83. Solved Problem 20 – Same Perimeter, Different Shapes

A square has perimeter 40 cm. Find its area.

Side:

[
a=\frac{40}{4}=10cm
]

Area:

[
10^2=100cm^2
]

Answer: 100 cm²

Now compare with a rectangle of length 15 cm and breadth 5 cm.

Perimeter:

[
2(15+5)=40cm
]

Area:

[
15\times5=75cm^2
]

So equal perimeter does not mean equal area.

84. Quick Concept Map

Think about mensuration as:

Shape

↓

What is being measured?

↓

Boundary → Perimeter

Surface → Area

Curved boundary → Circumference

Outer surface of solid → Surface Area

Space occupied → Volume

↓

Add unit correctly

This single mental map can prevent many mistakes.

85. Students Often Confuse These

Students Confuse	Correct Difference
Area and perimeter	Area covers surface; perimeter covers boundary
Radius and diameter	Diameter = 2 × radius
(m) and (m^2)	(m) is length; (m^2) is area
(m^2) and (m^3)	(m^2) is area; (m^3) is volume
Circumference and area of circle	Circumference is boundary; area is surface
Area of triangle and rectangle	Triangle = half of base × height
Semicircle area and perimeter	Perimeter includes diameter
Cuboid surface area and volume	Surface is outer covering; volume is space
Diameter used as radius	Convert diameter to radius first

86. Most Important Exam Traps

Trap 1: “Fencing”

Fencing means boundary.

Use perimeter.

Trap 2: “Tiling”

Tiling covers a surface.

Use area.

Trap 3: “Capacity”

Capacity of a tank generally requires volume followed by unit conversion.

Trap 4: Diameter Given

Use:

[
r=\frac d2
]

before using:

[
\pi r^2
]

Trap 5: Mixed Units

Convert all dimensions to the same unit first.

Trap 6: Area Units

Do not forget the square.

Trap 7: Volume Units

Do not forget the cube.

Trap 8: Four Walls

Do not include floor and ceiling unless specifically asked.

87. Fast Calculation Techniques

Competitive examinations reward speed, but speed should come from understanding.

Technique 1 – Simplify before multiplying

Instead of:

[
\frac{22}{7}\times14
]

first cancel:

[
14\div7=2
]

so:

[
22\times2=44
]

Technique 2 – Use familiar multiplication

For rectangle:

[
25\times16
]

think:

[
25\times(8\times2)
]

or use:

[
25\times100/4=625
]

Technique 3 – Memorise squares

Knowing squares up to 20 is extremely useful.

Technique 4 – Check the unit

A quick unit check often catches formula errors.

88. Estimation as a Safety Check

Suppose you calculate that a 20 m × 10 m field has area 2000 m².

Pause.

20 × 10 is approximately 200, not 2000.

So the calculation is obviously wrong.

This habit of estimating the answer before finalising it is excellent for competitive examinations.

89. Reverse-Checking Answers

Suppose:

Area = 240 cm²
Length = 20 cm

You calculate breadth = 12 cm.

Check:

[
20\times12=240
]

Correct.

Reverse-checking takes only a few seconds but can save a negative-marking mistake in an exam.

90. One-Look Formula Revision

Topic	Formula
Rectangle perimeter	(2(l+b))
Rectangle area	(lb)
Square perimeter	(4a)
Square area	(a^2)
Triangle area	(\frac12bh)
Parallelogram area	(bh)
Rhombus area	(\frac12d_1d_2)
Trapezium area	(\frac12(a+b)h)
Circle circumference	(2πr)
Circle area	(πr^2)
Semicircle area	(\frac12πr^2)
Cuboid volume	(lbh)
Cuboid LSA	(2h(l+b))
Cuboid TSA	(2(lb+bh+hl))
Cube volume	(a^3)
Cube LSA	(4a^2)
Cube TSA	(6a^2)

91. Super-Fast Memory Tricks

Rectangle

P = twice the sum

[
2(l+b)
]

A = length × breadth

[
lb
]

Square

P = 4 sides

[
4a
]

A = side × side

[
a^2
]

Triangle

Half base × height

[
\frac12bh
]

Circle

Boundary = 2πr

Area = πr²

Cuboid

Volume = three dimensions multiplied

[
lbh
]

Cube

Volume = edge three times

[
a^3
]

92. Mensuration Memory Map

MENSURATION
│
├── 2D FIGURES
│   ├── Rectangle
│   │   ├── P = 2(l+b)
│   │   └── A = lb
│   │
│   ├── Square
│   │   ├── P = 4a
│   │   └── A = a²
│   │
│   ├── Triangle
│   │   └── A = ½bh
│   │
│   └── Circle
│       ├── C = 2πr
│       └── A = πr²
│
└── 3D FIGURES
    ├── Cuboid
    │   └── V = lbh
    │
    └── Cube
        └── V = a³

93. Important Mensuration Facts for JKSSB Revision

Memorise these facts as one-liners:

Perimeter measures the boundary of a closed figure.
Area measures the surface occupied by a 2D figure.
Volume measures the space occupied by a solid.
Perimeter is expressed in linear units.
Area is expressed in square units.
Volume is expressed in cubic units.
Diameter is twice the radius.
Radius is half the diameter.
Area of rectangle = length × breadth.
Perimeter of rectangle = (2(l+b)).
Area of square = side².
Perimeter of square = 4 × side.
Area of triangle = half × base × perpendicular height.
Area of circle = πr².
Circumference of circle = 2πr.
(1m=100cm).
(1m²=10,000cm²).
(1m³=10,00,000cm³).
(1m³=1000L).
(1L=1000mL).
(1L=1000cm³).
(1 hectare=10,000m²).
Fencing normally requires perimeter.
Flooring normally requires area.
Painting a wall requires wall area.
Capacity of a cuboidal tank comes from volume.
Four walls of a room require lateral surface area.
A square is a special rectangle.
Equal perimeter does not guarantee equal area.
Equal area does not guarantee equal perimeter.

94. Important Comparison Table

Quantity	What to Imagine	Formula Example	Unit
Perimeter	Walking around boundary	(2(l+b))	m
Area	Covering surface	(lb)	m²
Circumference	Going around circle	(2πr)	m
Surface Area	Covering outside of solid	(6a²) for cube	m²
Volume	Filling inside/space	(lbh)	m³
Capacity	Liquid a container holds	volume conversion	L

95. Practical Applications of Mensuration

Mensuration is not artificial mathematics. It appears in everyday life.

Agriculture

Farmers may need to calculate:

field area
fencing length
irrigation tank capacity
land measurements

Construction

Builders calculate:

floor area
wall area
room dimensions
material requirements

Flooring

Tiles are purchased based on:

[
\text{Area to be covered}
]

Painting

Paint quantity is related to:

[
\text{Surface area}
]

Fencing

Wire or fencing material depends on:

[
\text{Perimeter}
]

Water Storage

Tank capacity depends on:

[
\text{Volume}
]

This real-life connection is exactly why mensuration is a recurring mathematical concept.

96. Conceptual Relationship Between Area and Volume

There is a useful hierarchy:

1D

Length

2D

Length × breadth

3D

Length × breadth × height

This can be remembered as:

[
\boxed{L}
]

[
\boxed{L^2}
]

[
\boxed{L^3}
]

where (L) represents a unit of length.

Therefore:

length → one dimension
area → two dimensions
volume → three dimensions

This explains why their units have different powers.

97. Why Unit Conversion Becomes Squared or Cubed

Suppose:

[
1m=100cm
]

For area:

[
1m^2=100cm\times100cm
]

[
=10000cm^2
]

For volume:

[
1m^3=100\times100\times100
]

[
=1,000,000cm^3
]

So the powers are not arbitrary. They come directly from the number of dimensions being measured.

98. Advanced but Useful Concept: Diagonal of Rectangle

Although not always required in a basic mensuration question, a rectangle's diagonal follows the Pythagorean theorem:

[
\boxed{d=\sqrt{l^2+b^2}}
]

Example:

Length = 3 cm
Breadth = 4 cm

[
d=\sqrt{3^2+4^2}
]

[
=\sqrt{9+16}
]

[
=\sqrt{25}
]

[
=5cm
]

This famous 3-4-5 relationship is useful for quick calculations.

99. Advanced but Useful Concept: Diagonal of a Square

For a square of side (a):

[
\boxed{d=a\sqrt2}
]

This comes from Pythagoras:

[
d^2=a^2+a^2
]

[
d^2=2a^2
]

[
d=a\sqrt2
]

This may be beyond a simple Class-IV-focused question, but it is useful knowledge when solving mixed-level competitive questions.

100. Common Mistakes to Avoid

Mistake 1

Using area when the question asks for fencing.

Mistake 2

Using perimeter when the question asks for flooring.

Mistake 3

Forgetting to convert cm to m.

Mistake 4

Writing (m) instead of (m²) for area.

Mistake 5

Writing (m²) instead of (m³) for volume.

Mistake 6

Using diameter as radius.

Mistake 7

Using slant height as triangle's perpendicular height.

Mistake 8

Forgetting the diameter in semicircle perimeter.

Mistake 9

Using total surface area when only four walls are required.

Mistake 10

Doing arithmetic before understanding the figure.

101. JKSSB Exam Strategy for Mensuration

For a serious JKSSB aspirant, the best strategy is not to memorise 30 formulas in isolation.

Instead, master the topic in this order:

Stage 1 – Basics

Learn:

units
perimeter
area
volume

Stage 2 – Core Shapes

Master:

square
rectangle
triangle
circle

Stage 3 – Solids

Master:

cube
cuboid

Stage 4 – Application

Practise:

fencing
flooring
painting
tank capacity
missing dimensions
unit conversion

Stage 5 – Objective Practice

Solve mixed MCQs where the figure is not explicitly named.

That final stage is important because exam questions rarely announce:

“This is a perimeter question.”

They expect you to recognise it from the wording.

102. How to Revise Mensuration in the Last Few Days

During final revision, create four columns mentally:

Remember	Understand	Watch	Practise
Formulas	Meaning of formula	Units	MCQs
Conversions	Boundary vs surface	Radius vs diameter	Word problems
Squares	Area vs volume	Semicircle perimeter	Mixed questions
Cubes	Four walls	Cost questions	Previous-style questions

A good final revision cycle is:

Formula → Example → Trap → MCQ

For every formula you learn, solve at least one question involving it.

103. Most Important “Exam Language” Decoder

This is worth revising immediately before a test.

Phrase	Think
Around	Perimeter
Boundary	Perimeter
Fence	Perimeter
Wire around	Perimeter
Cover	Area
Paint	Area
Tile	Area
Carpet	Area
Floor	Area
Land	Area
Surface	Area
Outside of solid	Surface area
Four walls	Lateral surface area
Space occupied	Volume
Filled with water	Volume/capacity
Holds	Capacity
Container	Volume/capacity

104. 40 JKSSB-Style Mensuration MCQs

MCQ 1

A rectangle has length 18 cm and breadth 7 cm. What is its area?

A. 25 cm²
B. 50 cm²
C. 126 cm²
D. 252 cm²

Answer: C. 126 cm²

Explanation:

[
A=l\times b=18\times7=126cm^2
]

MCQ 2

The perimeter of a square whose side is 15 cm is:

A. 30 cm
B. 45 cm
C. 60 cm
D. 225 cm

Answer: C. 60 cm

Explanation:

[
P=4a=4\times15=60cm
]

MCQ 3

A rectangular field is 30 m long and 20 m wide. Its perimeter is:

A. 50 m
B. 100 m
C. 600 m
D. 1200 m

Answer: B. 100 m

Explanation:

[
P=2(30+20)=100m
]

MCQ 4

The area of a square with side 12 m is:

A. 24 m²
B. 48 m²
C. 120 m²
D. 144 m²

Answer: D. 144 m²

Explanation:

[
A=12^2=144m^2
]

MCQ 5

The area of a triangle with base 16 cm and height 10 cm is:

A. 80 cm²
B. 160 cm²
C. 26 cm²
D. 320 cm²

Answer: A. 80 cm²

Explanation:

[
A=\frac12\times16\times10=80cm^2
]

MCQ 6

The diameter of a circle is 18 cm. Its radius is:

A. 36 cm
B. 9 cm
C. 6 cm
D. 3 cm

Answer: B. 9 cm

Explanation:

[
r=\frac d2=\frac{18}{2}=9cm
]

MCQ 7

The circumference of a circle is calculated using:

A. (\pi r^2)
B. (2πr)
C. (l\times b)
D. (a^2)

Answer: B. (2πr)

Explanation: Circumference is the boundary length of a circle.

MCQ 8

The area of a circle of radius 7 cm, using (π=22/7), is:

A. 44 cm²
B. 88 cm²
C. 154 cm²
D. 308 cm²

Answer: C. 154 cm²

Explanation:

[
A=\frac{22}{7}\times7^2=154cm^2
]

MCQ 9

1 metre is equal to:

A. 10 cm
B. 100 cm
C. 1000 cm
D. 10,000 cm

Answer: B. 100 cm

MCQ 10

1 square metre is equal to:

A. 100 cm²
B. 1000 cm²
C. 10,000 cm²
D. 1,00,000 cm²

Answer: C. 10,000 cm²

MCQ 11

1 cubic metre is equal to:

A. 1000 cm³
B. 10,000 cm³
C. 1,00,000 cm³
D. 10,00,000 cm³

Answer: D. 10,00,000 cm³

MCQ 12

The volume of a cuboid 8 cm long, 5 cm wide and 3 cm high is:

A. 16 cm³
B. 40 cm³
C. 120 cm³
D. 240 cm³

Answer: C. 120 cm³

Explanation:

[
V=8\times5\times3=120cm^3
]

MCQ 13

The area of a rectangular floor is generally required when calculating:

A. Fencing cost
B. Flooring cost
C. Boundary length
D. Walking distance

Answer: B. Flooring cost

MCQ 14

The cost of fencing a rectangular field is calculated using:

A. Area × rate
B. Perimeter × rate
C. Volume × rate
D. Side × side

Answer: B. Perimeter × rate

MCQ 15

A square has perimeter 48 cm. Its side is:

A. 8 cm
B. 10 cm
C. 12 cm
D. 16 cm

Answer: C. 12 cm

MCQ 16

A rectangle has area 200 cm² and length 20 cm. Its breadth is:

A. 5 cm
B. 10 cm
C. 20 cm
D. 40 cm

Answer: B. 10 cm

MCQ 17

Which of the following is a unit of area?

A. metre
B. centimetre
C. square metre
D. litre

Answer: C. square metre

MCQ 18

Which of the following is a unit of volume?

A. m
B. m²
C. m³
D. km

Answer: C. m³

MCQ 19

The perimeter of a rectangle with length 12 cm and breadth 8 cm is:

A. 20 cm
B. 40 cm
C. 96 cm
D. 192 cm

Answer: B. 40 cm

MCQ 20

The area of a rectangle with length 12 cm and breadth 8 cm is:

A. 20 cm²
B. 40 cm²
C. 96 cm²
D. 192 cm²

Answer: C. 96 cm²

MCQ 21

The area of a parallelogram with base 15 cm and perpendicular height 8 cm is:

A. 60 cm²
B. 120 cm²
C. 180 cm²
D. 240 cm²

Answer: B. 120 cm²

MCQ 22

The area of a rhombus with diagonals 10 cm and 14 cm is:

A. 24 cm²
B. 50 cm²
C. 70 cm²
D. 140 cm²

Answer: C. 70 cm²

MCQ 23

The area of a trapezium with parallel sides 10 cm and 16 cm and height 5 cm is:

A. 26 cm²
B. 52 cm²
C. 65 cm²
D. 130 cm²

Answer: C. 65 cm²

Explanation:

[
A=\frac12(10+16)\times5
]

[
=\frac12\times26\times5=65cm^2
]

MCQ 24

Which quantity is measured in litres?

A. Perimeter
B. Area
C. Capacity
D. Length

Answer: C. Capacity

MCQ 25

1 litre is equal to:

A. 100 mL
B. 500 mL
C. 1000 mL
D. 10,000 mL

Answer: C. 1000 mL

MCQ 26

A cuboid tank has dimensions 2 m × 1 m × 1 m. Its capacity is:

A. 20 L
B. 200 L
C. 2000 L
D. 20,000 L

Answer: C. 2000 L

Explanation:

[
V=2m^3
]

and:

[
1m^3=1000L
]

Therefore:

[
2m^3=2000L
]

MCQ 27

Which formula gives the area of a square?

A. (4a)
B. (2a)
C. (a^2)
D. (a^3)

Answer: C. (a^2)

MCQ 28

Which formula gives the volume of a cube?

A. (6a^2)
B. (4a)
C. (a^2)
D. (a^3)

Answer: D. (a^3)

MCQ 29

A room is 10 m long, 5 m wide and 4 m high. The floor area is:

A. 40 m²
B. 50 m²
C. 100 m²
D. 200 m²

Answer: B. 50 m²

MCQ 30

The area of four walls of a room depends on:

A. Only length
B. Only breadth
C. Length, breadth and height
D. Only floor area

Answer: C. Length, breadth and height

MCQ 31

If the radius of a circle is doubled, its area becomes:

A. 2 times
B. 3 times
C. 4 times
D. 8 times

Answer: C. 4 times

Explanation:

[
A=πr^2
]

Replacing (r) by (2r):

[
A'=π(2r)^2=4πr^2
]

MCQ 32

If the side of a square is doubled, its area becomes:

A. 2 times
B. 3 times
C. 4 times
D. 8 times

Answer: C. 4 times

MCQ 33

If all dimensions of a cuboid are doubled, its volume becomes:

A. 2 times
B. 4 times
C. 6 times
D. 8 times

Answer: D. 8 times

MCQ 34

A semicircle has radius 7 cm. Its area is:

A. 77 cm²
B. 154 cm²
C. 44 cm²
D. 22 cm²

Answer: A. 77 cm²

Explanation:

Full circle area:

[
154cm^2
]

Half:

[
77cm^2
]

MCQ 35

The perimeter of a semicircle includes:

A. Only curved part
B. Only diameter
C. Curved part and diameter
D. Radius only

Answer: C. Curved part and diameter

MCQ 36

A farmer wants to put fencing around a square field. Which measurement is required first?

A. Area
B. Perimeter
C. Volume
D. Height

Answer: B. Perimeter

MCQ 37

A floor is to be covered with tiles. Which quantity is most directly required?

A. Perimeter
B. Area
C. Circumference
D. Volume

Answer: B. Area

MCQ 38

A tank is filled with water. Which quantity determines how much water it can hold?

A. Perimeter
B. Area only
C. Volume/capacity
D. Circumference

Answer: C. Volume/capacity

MCQ 39

Which statement is correct?

A. Area is measured in metres
B. Perimeter is measured in square metres
C. Volume is measured in cubic units
D. Circumference is measured in litres

Answer: C. Volume is measured in cubic units

MCQ 40

The diameter of a circle is:

A. Half its radius
B. Equal to its radius
C. Twice its radius
D. Three times its radius

Answer: C. Twice its radius

105. Extra Challenge MCQs

MCQ 41

A rectangular field has perimeter 100 m and length 30 m. Its breadth is:

A. 10 m
B. 20 m
C. 30 m
D. 40 m

Answer: B. 20 m

Explanation:

[
100=2(30+b)
]

[
50=30+b
]

[
b=20m
]

MCQ 42

A square and a rectangle have the same perimeter of 40 cm. The square has side:

A. 5 cm
B. 8 cm
C. 10 cm
D. 20 cm

Answer: C. 10 cm

MCQ 43

A circle has diameter 28 cm. Its circumference is:

A. 44 cm
B. 66 cm
C. 88 cm
D. 154 cm

Answer: C. 88 cm

Explanation:

[
C=\pi d
]

[
=\frac{22}{7}\times28=88cm
]

MCQ 44

A rectangular plot is 50 m × 40 m. What is its area in hectares?

A. 0.02 hectare
B. 0.2 hectare
C. 2 hectares
D. 20 hectares

Answer: B. 0.2 hectare

Explanation:

Area:

[
50\times40=2000m^2
]

Since:

[
1ha=10000m^2
]

[
2000/10000=0.2ha
]

MCQ 45

A cube has edge 4 cm. Its volume is:

A. 16 cm³
B. 32 cm³
C. 64 cm³
D. 96 cm³

Answer: C. 64 cm³

MCQ 46

The total surface area of a cube of side 5 cm is:

A. 25 cm²
B. 50 cm²
C. 100 cm²
D. 150 cm²

Answer: D. 150 cm²

[
TSA=6a^2=6(25)=150cm^2
]

MCQ 47

A room measures 8 m × 5 m. The cost of flooring is ₹100 per square metre. Total cost is:

A. ₹4000
B. ₹5000
C. ₹8000
D. ₹13,000

Answer: B. ₹4000

Correction check:

Area:

[
8\times5=40m^2
]

Cost:

[
40\times100=₹4000
]

Therefore the correct answer is A. ₹4000.

This illustrates why checking the arithmetic is important even after selecting the correct method.

MCQ 48

A rectangular field is 20 m × 15 m. Fencing costs ₹10 per metre. Total fencing cost is:

A. ₹350
B. ₹500
C. ₹700
D. ₹3000

Answer: C. ₹700

Perimeter:

[
2(20+15)=70m
]

Cost:

[
70\times10=₹700
]

MCQ 49

The breadth of a rectangle is 10 cm and its area is 250 cm². The length is:

A. 15 cm
B. 20 cm
C. 25 cm
D. 30 cm

Answer: C. 25 cm

MCQ 50

Which one is correctly matched?

A. Fencing — Area
B. Flooring — Volume
C. Tank capacity — Volume
D. Wall painting — Perimeter

Answer: C. Tank capacity — Volume

106. Frequently Asked Conceptual Questions

Q1. What is mensuration?

Mensuration is the branch of mathematics dealing with the measurement of length, perimeter, area, surface area, volume and related quantities.

Q2. What is the difference between perimeter and area?

Perimeter is the total boundary length of a figure, whereas area is the surface covered by the figure.

Q3. What is the area formula of a rectangle?

[
A=l\times b
]

Q4. What is the perimeter formula of a rectangle?

[
P=2(l+b)
]

Q5. What is the area of a square?

[
A=a^2
]

Q6. What is the perimeter of a square?

[
P=4a
]

Q7. What is the area of a triangle?

[
A=\frac12bh
]

where (h) is the perpendicular height.

Q8. What is the circumference of a circle?

[
C=2πr
]

Q9. What is the area of a circle?

[
A=πr^2
]

Q10. What is the volume of a cuboid?

[
V=lbh
]

Q11. What is the volume of a cube?

[
V=a^3
]

Q12. How many centimetres are in one metre?

[
100cm
]

Q13. How many square centimetres are in one square metre?

[
10,000cm^2
]

Q14. How many litres are in one cubic metre?

[
1000L
]

Q15. What is the relation between radius and diameter?

[
d=2r
]

107. Students Often Confuse: Formula vs Meaning

Formula	Meaning
(2(l+b))	Boundary of rectangle
(lb)	Surface of rectangle
(4a)	Boundary of square
(a^2)	Surface of square
(\frac12bh)	Surface of triangle
(2πr)	Boundary of circle
(πr^2)	Surface of circle
(lbh)	Space of cuboid
(a^3)	Space of cube

This table is more useful than memorising formulas in random order.

108. One-Look Revision Before the Exam

RECTANGLE

[
P=2(l+b)
]

[
A=lb
]

SQUARE

[
P=4a
]

[
A=a^2
]

TRIANGLE

[
A=\frac12bh
]

CIRCLE

[
C=2πr
]

[
A=πr^2
]

CUBOID

[
V=lbh
]

[
LSA=2h(l+b)
]

[
TSA=2(lb+bh+hl)
]

CUBE

[
V=a^3
]

[
LSA=4a^2
]

[
TSA=6a^2
]

UNIT FACTS

[
1m=100cm
]

[
1m^2=10,000cm^2
]

[
1m^3=10,00,000cm^3
]

[
1m^3=1000L
]

[
1L=1000mL
]

[
1ha=10,000m^2
]

109. Final JKSSB Mensuration Revision Sheet

Before the examination, make sure you can answer these without hesitation:

Basic Concepts

What is perimeter?
What is area?
What is volume?
What is capacity?
What is surface area?

Rectangle

perimeter
area
missing length
missing breadth

Square

perimeter
area
missing side

Triangle

base
perpendicular height
area

Circle

radius
diameter
circumference
area
semicircle

Solid Figures

cube
cuboid
volume
surface area
tank capacity

Applications

fencing
flooring
painting
carpeting
land measurement
water tanks
cost calculations

Units

length
square units
cubic units
litres
millilitres
hectare

If all of these are comfortable, the foundation of mensuration is strong.

Number	Square
1	1
2	4
3	9
4	16
5	25
6	36
7	49
8	64
9	81
10	100
11	121
12	144
13	169
14	196
15	225
16	256
17	289
18	324
19	361
20	400

Number	Square
1	1
2	4
3	9
4	16
5	25
6	36
7	49
8	64
9	81
10	100
11	121
12	144
13	169
14	196
15	225
16	256
17	289
18	324
19	361
20	400

Mensuration for JKSSB Class IV – Complete Notes, Formulas, Solved Examples, Tricks & MCQs

Mensuration for JKSSB Class IV

1. What Is Mensuration?

2. Why Mensuration Matters in JKSSB Exams

Question

3. The Three Most Important Questions in Mensuration

Question 1: Am I measuring the boundary?

Question 2: Am I measuring the surface covered?

Question 3: Am I measuring the space occupied?

4. Perimeter – The Boundary of a Figure

Important idea

5. Rectangle

Perimeter of Rectangle

Example

Answer:

6. Area of a Rectangle

Example

7. Perimeter vs Area of Rectangle

Example

8. Square

Perimeter of Square

Area of Square

Example

9. An Important Relationship Between Square and Rectangle

10. Finding the Side of a Square from Its Perimeter

Shortcut

11. Finding the Side of a Square from Its Area

Important Square Roots to Remember

12. Triangle

Area of Triangle

Example

13. Why Is There a Half in the Triangle Formula?

14. Common Triangle Mistake

15. Parallelogram

Example

Important comparison

16. Rhombus

Example

17. Trapezium

Example

18. Circle

Radius

Diameter

19. Circumference of a Circle

20. Area of a Circle

Example

21. Circumference vs Area of Circle

22. Semicircle

Area

23. Quarter Circle

24. Circumference and Diameter: A Useful Relationship

Example

25. Units of Measurement

26. Important Length Conversions

27. Important Area Conversions

28. Important Volume Conversions

29. Quick Unit Revision Table

Very Important

30. Hectare and Square Metre

31. Three-Dimensional Figures

32. Cuboid

33. Volume of Cuboid

Example

34. Why Is Cuboid Volume (lbh)?

35. Capacity of a Cuboidal Tank

Answer:

36. Surface Area of a Cuboid

37. Lateral Surface Area of a Cuboid

38. Cube

Volume

Total Surface Area

Lateral Surface Area

Perimeter of one face

39. Cube Example

40. Formula Master Table

41. The Most Important Language Clues in Mensuration

Teacher's Tip

42. Cost-Based Mensuration Questions

Fencing

Flooring

Number	Square
1	1
2	4
3	9
4	16
5	25
6	36
7	49
8	64
9	81
10	100
11	121
12	144
13	169
14	196
15	225
16	256
17	289
18	324
19	361
20	400