Ex 12.3, 3
Find the area of the shaded region in figure, if ABCD is a square of side 14 cm and APD and BPC are semicircles.
Area of shaded region
= Area of square ABCD
Area of semicircle APD
Area of semicircle BPC
Area of square ABCD
Side of square = 14 cm
Area of square = Side Side
= 14 14
= 196 cm2
Area of semi circle APD
Diameter = AD = 14 cm
So, radius = /2 = 14/2 = 7 cm
Area of semi circle APD = 1/2 r2
= 1/2 22/7 7^2
= 1/2 22/7 7 7
= 77 cm2
Similarly,
For semicircle BPC
Diameter = BC = 14 cm
Since diameter is same
Area of semi circle BPC = Area of semi circle APD = 77 cm2
Now,
Area of shaded region
= Area of square
Area of semi circle APB Area of semi circle BPC
= 196 77 77
= 196 (77 + 77)
= 196 (154)
= 42 cm2
Hence, area of shaded region = 42 cm2

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.