Mensuration Formula, Definition, Rules, Sample Questions, Tips and FAQs

Quantitative Aptitude Prep Tips for MBA 2024

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Vipra Shrivastava

Vipra ShrivastavaSenior Manager - Content

Updated on Feb 5, 2024 18:44 IST

What is Mensuration?

Mensuration can be defined as the measurement of geometric figures such as quadrilaterals, their areas, perimeter, surface areas, and volumes. It is a very important topic in CAT and other MBA entrance exams. Mensuration questions are also asked in other competitive exams, so if you are preparing for any entrance or competitve exam, then you must prepare Mensurarion thoroughly.

Mensuration Formulas

Trapezium:

A trapezium is outlined by a form that has 2 parallel sides and the other 2 are nonparallel. It has four sides and four vertices.

Mensuration formula Trapezium
 

Shape

Area

Perimeter

1. Trapezium

Area= (1/2) H + (AB+CD)

P= sum of all the sides i.e. AB+BC+CD+AD

2. General quadrilateral

Area= Area of △ABC + Area of △ADC

The perimeter depends on the type of shape which is present

3. Special quadrilateral (rhombus)

½ × d1 × d2

P=4a

Where, H= height, W= breadth, a,b,c,d= sides, d= diagonals.

Mensuration formula quadrilateral

Surface area: It is the the total area of all the surfaces of any form.

Volume: the degree is outlined by the number any third-dimensional form takes.

measurement of a cuboid

Measurement of a cuboid

Solid shapes:

Solid shapes are measured by their three-dimensional structure with outlined breadth, height and length. A cube, sphere, cylinder, cuboid are solid shape examples.

Mensuration solid shapes

 

Shape

Surface area

Volume

1.    Cube

Area= 6a^2

V= a^3

2.    Cuboid

Area= 2 [(l × b) + (l× h) + (b× h)]

V= l*w*h

3.    Cylinder

Ares= 2πr (r + h)

V= πr2 × h

Where, H= height, a= sides, r= radius, d= diameter, b= breadth, w= width

Also Read: MBA Preparation 2024: Tips to Prepare for MBA Entrance Exams

Illustrated Examples of Mensuration Formulas

Example 1: Calculate the area of a rhombus whose diagonals are 10 cm and 8.2 cm of length. 

Ans: The formula for calculating area of a rhombus = ½ d1d2, (d1 and d2 are the lengths of the diagonal)

a= 2 × 10 × 8.2 cm2 = 41 cm2.

Example 2: A rhombus with an area of 240cm2 and whose one diagonal is of length 16 cm. Find the other diagonal.

Ans: We know d1 = 16 cm and let the other diagonal = d2

Thus the area of the rhombus = 2 d1 . d2 = 240

So, ½ 16 d2 = 240

Therefore, d2= 30cm

Diagonal 2 is 30 cm.

Also Read:

VARC Preparation Tips for MBA Exams DILR Preparation Tips for MBA Exams

Example 3: A cuboid-shaped aquarium is a present whose external measurements are of 80 cm × 30 cm × 40 cm. The base, side faces and back face are to be covered with a coloured paper. Find the area of the paper needed?

Ans: The length of the aquarium = l = 80 cm

Width of the aquarium  (b) = 30 cm

Height of the aquarium  (h) = 40 cm

Thus the area of the base = 80 × 30 = 2400 cm2

Area of the side face = 30 × 40 = 1200 cm2 &

Area of the back face = 80 × 40 = 3200 cm2

Thus area required to be calculated = Area of the base + area of the back face + (2 × area of a side face)

=  2400 + 3200 + (2 × 1200) = 8000 cm2

Read More:

CAT Quantitative Aptitude Questions for Practice with Solutions

FAQs Related to Mensuration and Mensuration Formulas

Q: What is the formula of the area of a cube?

A: The Formula for area of sq. can be: Area=6a^2 Where a= sides of the cube

Q: What is the area of the quadrilateral?

A: The area of the quadrilateral depends on the form of that specific quadrilateral. Example: area of general quadrilateral = space of △ABC + Area of △ADC.

Q: What is the height of a cylindrical structure?

A: The height of a cylinder is calculated by multiplying the world of the cylinder’s base (the circle) with its height.

Q: How many edges and faces will a cuboid have?

A: A cuboid has 6 faces, 12 edges.

Q: What is the area of a cuboid?

A: Surface area= Area= two [(l × b) + (l× h) + (b× h)] Where, l= length, h=height, b= breadth

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