Mensuration Class 6 Notes Maths Chapter 9

What is Mensuration?

Mensuration is a branch of mathematics that is a topic in Geometry. It is a study of various geometrical shapes, their length, breadth, volume, and area for 2D as well as 3D shapes.

Some important terminologies included in this topic are covered below.

Perimeter

Perimeter is the distance covered along the boundary forming a closed figure when we go around the figure once. The concept of the perimeter is widely used in real life. For Example: 

1. For fencing land.
2. For building a compound wall around a house.

Closed figure

• A figure with no open ends is a closed figure.
• Regular closed figures: A closed figure with all sides and angles equal.
• The perimeter of a regular closed figure is equal to the sum of its sides.

Perimeter of a Rectangle:

= 2 (l + b)

Example 1:  A rectangle has a length of 5 units and a breadth of 3 units.
Solution: 

Perimeter = 2(length + breadth)
= 2(5 + 3)
= 2(8)

 = 16 units

Example 2: A rectangular garden has a length of 15 meters and a breadth of 7 meters. Find the perimeter of the garden.

The perimeter of a rectangle is given by the formula P = 2(l + b), where l is the length and b is the breadth.
l = 15 meters
b = 7 meters
So, the perimeter is P = 2(15 + 7)
= 2(22) 

= 44 meters

Perimeter of a Square:

= 4 x S

Example 1: A square has a side length of 4 units.

Perimeter = 4 * side
length = 4 * 4 

= 16 units

Example 2: A square photo frame has a side length of 8 centimeters. Find the perimeter of the photo frame.

The perimeter of a square is given by the formula P = 4s, where s is the side length.
s = 8 centimeters
So, the perimeter is P = 4(8)
= 32 centimeters

Perimeter of an Equilateral triangle:

The perimeter of an equilateral triangle with the side 'a'=a+a+a =3 x a

Example 1: An equilateral triangle has a side length of 6 units.

Perimeter = 3 * side length
= 3 * 6
= 18 units

Example 2: An equilateral triangle has a side length of 10 inches. Find the perimeter of the triangle.

The perimeter of an equilateral triangle is given by the formula P = 3s, where s is the side length.
s = 10 inches
So, the perimeter is P = 3(10) 

= 30 inches

Area

The amount of surface enclosed by a closed figure is called its area. The following conventions are to be adopted while calculating the area of a closed figure using a squared or graph paper.

• Count the fully-filled squares covered by the closed figure as one square unit or unit square each.
• Count the half-filled squares as half a square unit.
• Count the squares that are more than half-filled as one square unit.
• Ignore the squares filled less than half.

For example, the area of this shape can be calculated as shown:

• Area covered by full squares = 6 x 1 = 6 sq. units Area covered by half squares = 7 x ½ = 7/2= 3 ½ sq. units.
• Total area of the given shape = 6 + 3 ½ sq. units Thus, the total area of the given shape = 9 ½ sq. Units.

Area of a Rectangle

The area of the rectangle can be obtained by multiplying the length by the breadth. 

Area = length ( l ) × breadth ( b)

Example: Find the area of a rectangle with a length 8 units and breadth 5 units.

The formula for the area of a rectangle is
A = length × breadth
A = 8 × 5
A = 40 square units

Area of a Square

The area of the square can be obtained by multiplying side by side. 

Area of a square = Side × Side =Side2=a2, where a is the length of each side.

Example: Find the area of a square with a side length of 6 units.

The formula for the area of a square is
A = side × side
A = 6 × 6
A = 36 square units

Area of a Triangle

Area of triangle = (1/2) × base × height = (1/2) × b × h 

Example: Find the area of a triangle with a base of 10 units and height of 4 units.

The formula for the area of a triangle is
A = (1/2) × base × height.
A = (1/2) × 10 × 4
A = 20 square units

Summary