Mensuration is the part of math that helps us measure shapes and objects around us.
It tells us how to find things like length, area, volume, and surface area for different figures—like squares, rectangles, circles, cubes, and cylinders.

We use it in real life too, like when we want to know how much space is inside a box or how much paint we need to cover a wall.

Table of Contents:

• Definition
• Important Terms
• Formulas
  • 2D Shapes
  • 3D Shapes
• Solved Problems
• Practice Questions

Mensuration Maths- Definition

Mensuration is a part of math that helps us measure the length, area, or volume of different shapes. These shapes can be flat (2D), like squares and circles, or solid (3D), like cubes and cylinders. Mensuration tells us how much space a shape covers or holds. In this topic, we learn how to work with both 2D and 3D shapes using simple formulas to find their measurements.

Mensuration in Maths- Important Terminologies

Let’s familiarize ourselves with a few more definitions associated with this subject.

Terms	Abbreviation	Unit	Definition
Area	A	m2 or cm2	The area refers to the surface covered by a closed shape.
Perimeter	P	cm or m	The perimeter is the measure of the continuous line along the boundary of a given figure.
Volume	V	cm3 or m3	The volume is the space occupied by a 3D shape.
Curved Surface Area	CSA	m2 or cm2	The Curved Surface area is the total area of a curved surface, such as a sphere.
Lateral Surface area	LSA	m2 or cm2	The Lateral Surface area is the total area of all the lateral surfaces that surround a given figure.
Total Surface Area	TSA	m2 or cm2	The Total Surface area is the sum of all the curved and lateral surface areas.
Square Unit	–	m2 or cm2	A Square unit is the area covered by a square with sides of one unit.
Cube Unit	–	m3 or cm3	A Cube unit is the volume occupied by a cube with sides of one unit.

Mensuration Formulas

Now let’s delve into all the essential mensuration formulas for 2D and 3D shapes. These formulas will help you solve mensuration problems with ease. The most common formulas in mensuration typically involve the surface area and volumes of 2D and 3D figures.

Mensuration Formulas For 2D Shapes

Below, you’ll find the mensuration formulas for two-dimensional geometric shapes.

Shape	Area (Square units)	Perimeter (units)	Figure
Square	a2	4a
Rectangle	l × b	2 ( l + b)
Circle	πr2	2 π r
Scalene Triangle	√[s(s−a)(s−b)(s−c)], Where, s = (a+b+c)/2	a+b+c
Isosceles Triangle	½ × b × h	2a + b
Equilateral triangle	(√3/4) × a2	3a
Right Angle Triangle	½ × b × h	b + hypotenuse + h
Rhombus	½ × d1 × d2	4 × side
Parallelogram	b × h	2(l+b)
Trapezium	½ h(a+c)	a+b+c+d

Mensuration Formulas for 3D Shapes

Here are the mensuration formulas for three-dimensional shapes in geometry.

Shape	Volume (Cubic units)	Curved Surface Area (CSA) or Lateral Surface Area (LSA) (Square units)	Total Surface Area (TSA) (Square units)	Figure
Cube	a3	LSA = 4 a2	6 a2
Cuboid	l × b × h	LSA = 2h(l + b)	2 (lb +bh +hl)
Sphere	(4/3) π r3	4 π r2	4 π r2
Hemisphere	(⅔) π r3	2 π r2	3 π r2
Cylinder	π r2 h	2π r h	2πrh + 2πr2
Cone	(⅓) π r2 h	π r l	πr (r + l)

Also, Check out the Latest Railway Exams with Maths as a Part of its Syllabus

Mensuration Solved Problems

Question 1:

Find the area and perimeter of a rectangle with length 8 cm and width 4 cm.

Solution:

Given:
Length = 8 cm
Width = 4 cm

 Area of rectangle = length × width
= 8 × 4 = 32 cm²

 Perimeter of rectangle = 2 × (length + width)
= 2 × (8 + 4) = 2 × 12 = 24 cm

Answer:
Area = 32 cm², Perimeter = 24 cm

Question 2:

Find the area of a triangle with base 10 cm and height 6 cm.

Solution:

Given:
Base = 10 cm
Height = 6 cm

 Area of triangle = (1/2) × base × height
= (1/2) × 10 × 6 = 30 cm²

Answer:
Area = 30 cm²

Question 3:

Find the circumference and area of a circle with radius 7 cm.

Solution:

Given:
Radius (r) = 7 cm

 Circumference = 2πr
= 2 × (22/7) × 7 = 44 cm

 Area = πr²
= (22/7) × 7 × 7 = 154 cm²

Answer:
Circumference = 44 cm, Area = 154 cm²

Question 4:

Find the diagonal of a square with side length 6 cm.

Solution:

Given:
Side (a) = 6 cm

 Diagonal of square = a√2
= 6√2 cm

Answer:
Diagonal = 6√2 cm

Practice Questions

1.Find the area of a rectangle with Length = 15 cm,Breadth = 12 cm.

2.Calculate the volume of a right circular cylinder with Radius = 7 cmHeight = 24 cm.

3.Find the curved surface area (CSA) of a cylinder with Radius = 5 cmHeight = 10 cm.

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