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Question
In the given figure `square`ABCD is a square of side 50 m. Points P, Q, R, S are midpoints of side AB, side BC, side CD, side AD respectively. Find area of shaded region
Solution
Area of square ABCD = (side)2
= (50)2
= 2500 m
Radius of sector A–SP = `1/2 xx 50` = 25 m
θ = 90° ......[Angle of a square]
Area of sector A–SP = `θ/360 xx π"r"^2`
= `90/360 xx 22/7 xx (25)^2`
= `(1/4 xx 13750/7)` m2
A(shaded region) = Area of square ABCD – 4(Area of sector A–SP)
= `2500 - 4(1/4 xx 13750/7)`
= `2500 - 13750/7`
= `(17500 - 13750)/7`
= `3750/7`
≈ 535.71 m2
∴ Area of the shaded region is 535.71m2
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