Quick Tips on How to Prepare Mensuration

By Nitin Singhal|Updated : February 26th, 2021

Mensuration basically means 'Measurement' and this segment of Elementary mathematics involves the measurement of areas, volumes, lengths, etc of the given figures. In this post, we have covered some important tips to prepare Mensuration for the State exams.

Out of the 100 questions of the Mathematics section, mensuration usually accounts for 12-15 questions in the State exams and hence, one must be thorough with the concepts and important formulas of Mensuration for the State exam, to score well in its Mathematics section.

How to Prepare Mensuration?

Mensuration can be broadly categorized into 2 segments, namely:
(a) 2-D Mensuration
(b) 3-D Mensuration

As the name suggests, 2-D Mensuration deals with the computation of areas/ volumes/ lengths of 2-dimensional figures like Squares, Rectangles, Rhombus, Circle, Parallelogram, Trapezium etc while 3D mensuration is for figures like Cubes, Cuboids, Cone, Cylinder, Sphere, etc.
In order to solve the questions of Mensuration for the State exam, one must be well-versed with its commonly used formulas. We will now cover both 2D & 3D Mensuration for the State exam.

Important formulas for 2-D Mensuration

Figure & its Diagram

Commonly Used Formulas

1. Rectangle


(a) Area = l x b

(b) Perimeter = 2 (l + b)

(c) Length of Diagonal = √l2 + b2

2. Square


(a) Area = a2

(b) Perimeter = 4*a

(c) Length of Diagonal = a*√2

3. Parallelogram


(a) Area = l x h

(b) Perimeter = 2*(l + b)

4. Triangle


(a) Area of right-angled triangle = ½ *b*h

(b) Area of Scalene triangle (sides a, b, c) =
s = (a + b + c)/ 2 (s = semi-perimeter)
Area = √ {s (s-a) (s-b) (s-c)}

(c) Area of Isosceles triangle
= b/4 *√(4a2 – b2)

(d) Area of Equilateral triangle
= √3/4 * a2

5. Trapezium


(a) Area = ½*(AB + CD)*AE

(b) Perimeter = Sum of all sides

6. Rhombus


(a) Area = ½ *(Product of diagonals) = ½d1d2

(b) Perimeter = 4*l

7. Circles


(a) Area = πr2

(b) Circumference = 2πr 

(c) Length of Arc AB = (2πrθ)/360
(where θ is the angle at the centre)

(d) Area of sector AOB
= (1/2) × (length of arc) × r = (πr2θ)/360

Important Formulas for 3-D Mensuration

Figure & its Diagram

Commonly Used Formulas

1. Cube


(a) Volume = a3

(b) Total Surface Area = 6a2

(c) Length of diagonal through centre = a*√3

2. Cuboid


(a) Volume = l*b*h

(b) Total Surface Area = 2*(lb + bh + hl)

(c) Length of diagonal through centre
= √l2 + b2 + h2

3. Cone


(a) Volume = 1/3 * πr2h

(b) Total Surface Area = π*r*(l + r)

(c) Curved Surface Area = π*r*l

(d) Slant height = √(h2+r2)

4. Cylinder


(a) Volume = πr2h

(b) Total Surface Area = 2πr*(h + r)

(c) Curved Surface Area = 2πrh

5. Sphere & Hemisphere


(a) Volume of Sphere = (4/3) πr3
(b) Surface area of Sphere = 4πr2
(c) Volume of Hemisphere = (2/3) *πr3
(d) Total Surface area of Hemisphere = 3πr2
(e) Curved Surface Area of Hemisphere = 2πr2

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