﻿ Mensuration - Class 6 Maths Chapter 9 Question Answer

# Mensuration

## Mensuration - Sub Topics

The learning objectives of this chapter in mathematics typically include understanding the fundamental concepts of mensuration which include perimeter, area, volume, etc. and the relationships among them.

• Mensuration
• Perimeter
• Area
• Solved Questions on Mensuration
• ## Mensuration

Mensuration is a branch of mathematics that deals with the measurement of geometric quantities such as length, perimeter, area, volume and angles. It has numerous applications in both mathematics and everyday life.

### Perimeter

The perimeter of a shape is the sum of all the distances along its boundary. In mathematical terms, it is denoted by the symbol 'P'.

Perimeter = Sum of all sides

The units of measurement used for expressing perimeter can include centimetres (cm), metres (m) and other length units.

### Area

Area is the quantity of space contained within a closed shape. In mathematical terms, it is denoted by the symbol 'A'.

The units of measurement used for expressing area can include square centimetres (cm²) and square metres ().

Example:  What is the area of the square PQRS if the perimeter of a square PQRS is twice the perimeter of XYZ?

a) 42.25 cm2
b) 42.75 cm2
c) 52.25 cm2
d) 52.75 cm2

Explanation: Perimeter of △XYZ
= XY + YZ + YZ
= 5.5 + 3.55 + 3.95
= 13 cm

Perimeter of a square PQRS is twice the perimeter of △XYZ.

Perimeter of a square PQRS = 2 × Perimeter of △XYZ
⇒ 4 × Side = 2 × 13 cm
⇒ 4 × Side = 26 cm
⇒ Side = 26 cm/4
⇒ Side = 6.5 cm

Area of a square = Side × Side

= 6.5 cm × 6.5 cm
= 42.25 cm2

## Steps for calculating the area of a figure using squared paper

1. Begin by outlining the shape's perimeter on a square grid paper.
2. Disregard any area that is less than half a square in size.
3. If more than half a square lies within the shape, count it as a whole square.
4. When exactly half of a square is within the shape, consider its area as ½ square unit.
5. Finally, sum up these counted squares and halves to determine the area of the given enclosed shape.

The figure shows the area of a figure using squared paper.

Example: What is the difference in the area of the given shapes?

a) 1 cm2
b) 2 cm2
c) 3 cm2
d) 4 cm2

Explanation: Area of each square = 1 cm × 1 cm = 1 cm2

For First Figure:

 Square covered by the figure Number of squares (Estimated) Area Full-filled squares 6 6 × 1 cm2 = 6 cm2 More than half squares 8 8 × 1 cm2 = 8 cm2

Total area = 6 cm2  + 8 cm2  = 14 cm2
For Second Figure:

 Square covered by the figure Number of squares (Estimated) Area Full-filled squares 9 9 × 1 cm2 = 9 cm2 More than half-filled squares 9 9 × 1 cm2 = 9 cm2

Total area = 9 cm2 + 9 cm2 = 18 cm2

Difference in their area = Area of second figure − Area of first figure
= 18 cm2   − 14 cm2
= 4 cm2