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Question
In the figure given below, ABCD is the rectangle. AB = 14 cm, BC = 7 cm. From the rectangle, a quarter circle BFEC and a semicircle DGE are removed. Calculate the area of the remaining piece of the rectangle. (Take `pi = 22/7`).
Solution
Considering the given figure:
Given dimensions of the rectangle: AB = 14 cm and BC = 7 cm
⇒ Radius of the quarter circle = 7 cm
Area of the quarter circle
= `1/2 xx 22/7 xx 7^2` sq. cm
`= 77/2` sq. cm
Since EC = 7 cm and DC = 14 cm, we have
Therefore, radius of the semi circle = `7/2` cm
Area of the semi circle = `1/2 xx 22/7 xx (7/2)^2` sq. cm
= `77/4` sq. cm
Now, are of rectangle ABCD = AB x BC = 14 x 7 = 98 sq. cm
∴ Required area = Area of rectangle ABCD - [Area(BCEF) + Area(DGE)]
`= 98 - 77/2 - 77/4`
`= 161/4`
= 40.25 sq. cm
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