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Find the area of the shaded design in Fig. 12.17, where ABCD is a square of side 10 cm and semicircles are drawn with each side of the square asdiameter. |
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Answer» If we look closely at the given figure, we can see, Area of 4 semi circles = Area of shaded region + Area of square `ABCD` So, Area of shaded region,`A_S` = Area of 4 semi circles - Area of square `ABCD` Here, Radius of circle, `r = (CD)/2 =10/2 = 5cm` Area of semi-circle, `= 1/2pir^2 ` So, area of 4 semi-circles, `A_(SC) = 4*1/2pir^2 = 2pir^2 = 2**3.14**5**5` `A_(SC) = 157cm^2` Now, Area of square, `A_(SQ) = CD^2 = 100cm^2` So, Area of shaded region, `A_(S) = 157-100 = 57cm^2` |
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