Mensuration: Overview, Questions, Preparation

Mensuration 2021 ( Mensuration )

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Rachit Kumar Saxena

Rachit Kumar SaxenaManager-Editorial

Table of Contents
  1. What is Mensuration?
  2. Weightage and Importance of Mensuration 
  3. Illustrated example on Mensuration
  4. FAQs on Mensuration

What is Mensuration?

Mensuration is the measurement of geometric figures. This chapter will learn about some additional quadrilaterals, their areas, perimeter, surface areas, and volumes.

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.

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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

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Quadrilateral

Surface area: The definition is that the total area of all the surfaces of any form.
Volume: the degree is outlined by the number any third-dimensional form takes.

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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.

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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

Weightage and Importance of Mensuration 

The chapter Mensuration is in class 8. It is chapter 11 of NCERT textbook. The weightage is 15% of the total marks. 

Illustrated example on Mensuration

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

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.

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

Solution:

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.

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?

Solution: 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

FAQs on Mensuration

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
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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 vi 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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