Mathematics

In the figure (ii) given below, ABCD is a square of side 14 cm. Find the area of the shaded region.

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Let radius of each circle be r cm.

From figure,

⇒ r + r + r + r = 14

⇒ 4r = 14

⇒ r = 3.5 cm.

Since, radius is same so, each circle will have same area.

Area of each circle = πr²

= $\dfrac{22}{7} \times (3.5)^2$

= $\dfrac{22}{7} \times 3.5 \times 3.5$

= 22 × 0.5 × 3.5

= 38.5 cm²

Area of square = (side)² = 14² = 196 cm².

Area of shaded region = Area of square - Area of circles

= 196 - 4 × 38.5

= 196 - 154

= 42 cm².

Hence, area of shaded region = 42 cm².

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