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.

Explanation

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`

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