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Example 5: Find the area of a square whose length is 14 cm. 14 cm
Solution: Length of a side of the square = 14 cm

Area of the square = side × side 14 cm
= 14 cm × 14 cm = 196 sq. cm
Example 6: Find the area of a square whose perimeter is 84 cm.
Solution: Perimeter of the square = 84 cm

Side of the square = Perimeter of the square ÷ number of sides
= (84 ÷ 4) cm = 21 cm

Now, area of the square = side × side
= (21 × 21) sq. cm = 441 sq. cm
Thus, the area of the square is 441 sq. cm.

Think Tank Critical Thinking
What will be the length of the side of a square whose area and perimeter are equal?

FACTS
Two rectangles can have the same perimeter but very different areas. A long, skinny rectangle
such as 1 cm by 9 cm has a perimeter of 20 cm and an area of 9 sq. cm. On the other hand, a square-
like rectangle such as 5 cm by 5 cm also has a perimeter of 20 cm, but its area is much larger, i.e.,
25 sq. cm.

AreA of A CompoSite figUre

Example 1: Find the area of the following figure.

5 cm 1 cm

3 cm
1 cm

5 cm
Solution: The given figure can be divided into three rectangles as (I) 1 cm
shown.

Area of rectangle (I) = 5 cm × 1 cm = 5 sq. cm 1 cm 3 cm

Area of rectangle (II) = 3 cm × 1 cm = 3 sq. cm (II)
Area of rectangle (III) = 5 cm × 1 cm = 5 sq. cm
(III)
Area of the complete figure

= area of rectangle (I) + area of rectangle (II) + area of rectangle (III)
= 5 sq. cm + 3 sq. cm + 5 sq. cm = 13 sq. cm

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