Question

Calculate the area of the shaded region, if the diameter of the semi-circle is equal to 14 cm. (Take π = 22/7).

Answer 1

AC = DE = 14 cm     ...(Given)
AB = BC = 7 cm       ...(Given)

Area of the shaded region = Area of rectangle ACDE + Area of semicircle DEF - 2 x Area of quadrant 
∴ Area of rectangle = Length x Breadth
Area of semicircle = `1/2`πr²
2 x Area of quadrant = `π/4` (r²)

∴ Area of the shaded region = 14 x 7 + `π/2 (7)^2 - 2 xx π/4 (7)^2`

= 98 + `(49π)/2 - (49π)/2`
= 98 cm².