Page 172 - Math Skill - 5

170 Maths

Area of Composite Figures having Rectangles and Squares
We have learnt how to find the area of a square and a rectangle. But every figure cannot be as
simple as a square or a rectangle. There are figures which are formed by the combination of two
or more rectangles or squares or both.

Area of such figures is determined by separating all the squares and rectangles, calculating
their areas and then adding up.

Let’s Attempt
Example 1: Find the area of the adjoining figure.

Solution: The adjoining figure is the floor of an L-shaped
room. To find the area of this floor, we divide it
into two rectangles marked as P and Q and find the
area of each rectangle separately and then add the
two to find the area of the total floor.

Thus, area of the rectangle P = 8 m × 5 m = 40 sq m
Area of rectangle Q = 3 m × 1.5 m = 4.5 sq m

Total area of the floor = (40 + 4.5) sq m = 44.5 sq m.

The area of the figure is 44.5 sq m.
Example 2: The figure alongside shows a rectangular park with
a pathway around it (shown as shaded). Length

and breadth of the park along with pathway are 21 m 24 m 15 m
27 m and 21 m respectively. Excluding the
pathway, length and breadth of the park are 24 m
and 15 m respectively. Find the area of the pathway. 27 m
Solution: Area of the park including the pathway = Length × Breadth

= 27 m × 21 m = 567 m 2

Area of the park excluding pathway = Length × Breadth
= 24 m × 15 m = 360 m 2
Area of the pathway

= Area of the park including pathway – Area of the park excluding pathway

= 567 m – 360 m = 207 m .
2
2
2
The area of the pathway is 207 m .
2
Example 3: Find the area of the figure shown on the next page.
Solution: The figure shown is made up of 3 rectangles marked as P, Q and R.

For rectangle P: Length = 12 cm, Breadth = 6 cm
For rectangle Q: Length = 12 cm, Breadth = 6 cm