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Area of a Rectangle

As we saw earlier, the area of a shape can be found by counting the number of squares inside the shape.

The area of a rectangle can be found the same way, i.e. by counting the number of squares of unit length inside the rectangle.

Let us look at the following three rectangles. The first rectangle has a length of 4 cm and breadth of 3 cm. Drawing lines of unit length (here 1 cm) inside the rectangle gives us a number of squares of unit dimension. The area of the rectangle is obtained by simply counting the number of squares within the rectangle – for the first rectangle it is 12 sq cm. Similarly the area of rectangle 2 and 3 is 6 sq cm and 8 sq cm respectively.

From these examples, we can see the area is obtained by multiplying the number of squares along the length by the number of squares along the breadth. This leads us to the formula to find the area of a rectangle much more easily.

The area of a rectangle A with length l units and breadth b units is given by the formula

A = l x b

Note that the rectangle is different to a square in that the length and breadth of the rectangle are of different dimensions, and the difference in the formula for area of a square.

 

Area A = l x b     area of rectangle=12 sq cm

=  4 x 3

=  12 sq cm

 

 

Area A = l x b     area of rectangle=6 sq cm

=  2 x 3

=  6 sq cm

 

 

Area A = l x b     area of rectangle=8 sq cm

=  2 x 4

=  8 sq cm

 

 

Example 1: What is the area of a rectangle with the lengths of their sides 6 mm and 4 mm?

A = l x b

=  6 x 4

= 24 mm2

 

Example 2: What is the value of the pronumeral in this figure, given the area of the rectangle is 32 cm2?

A = l x b     area of rectangle=32 sq cm

32 =  8 x k

k =  32 ÷ 8

= 4 cm

 

Let us look at calculating the area of a square and rectangle in a composite shape.