Find the area of the shaded region where abcd is a square of side 10 cm and semicircles are drawn

Text Solution

Solution : If we look closely at the given figure, we can see,<br> Area of 4 semi circles = Area of shaded region + Area of square `ABCD`<br> So, Area of shaded region,`A_S` = Area of 4 semi circles - Area of square `ABCD`<br> Here, Radius of circle, `r = (CD)/2 =10/2 = 5cm`<br> Area of semi-circle, `= 1/2pir^2 `<br> So, area of 4 semi-circles, `A_(SC) = 4*1/2pir^2 = 2pir^2 = 2**3.14**5**5`<br> `A_(SC) = 157cm^2`<br> Now, Area of square, `A_(SQ) = CD^2 = 100cm^2`<br> So, Area of shaded region, `A_(S) = 157-100 = 57cm^2`<br>