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Question
In the given figure, a rectangle ABCD is inscribed inside a semi-circle of radius 10 cm. Using the dimensions given in the figure, determine the area of the shaded region.
Solution
From the figure, ABCD is the rectangle inscribed in the semi-circle with centre O.
Area of rectangle ABCD = `l xx b`
= AB × BC
= 14 × 7
= 98 cm2
The radius of semi-circle PABQ = 10 cm
Area of semi-circle PABQ = `1/2πr^2`
= `1/2 xx 22/7 xx (10)^2`
= `2200/14`
= 157.14 cm2
Area of the shaded region – Area of semi-circle PABQ – Area of rectangle ABCD
= 157.14 – 98
= 59.14 cm2
Hence, the area of the shaded region is 59.14 cm2.
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