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Question

In given figure, PQRS is a square of side 4 cm. Find the area of the shaded square.
973568_e65b2b9d6d08465e90febebc85e77bb9.png

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Solution

Here, r=1cm,θ=90o and a=4cm

Area of 4 sectors =4×θ360oπr2

Area of 4 sectors =4×90o360o×3.14×(1)2

Area of 4 sectors =4×3.14×14=3.14cm2

Area of circle =πr2=3.14×(1)2=3.14cm2

Area of a square =a2=(4)2=16cm2

Area of shaded region = Area of square - (Area of 4 sectors + Area of circle)

Area of shaded region =16(3.14+3.14)

Area of shaded region =166.28=9.72cm2

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