Question

Calculate the area of the shaded region in figure, common between the two quadrants of circle of radius $8cm$ each.

Answer 1

Area of designed region$=$ Area of first quadrant$+$Area of second quadrant$-$Area of square.

$=\frac{\theta }{360}\times \pi r^2+\frac{\theta }{360}\times \pi r^2-side\times side$

$=2\frac{\theta }{360}\times \pi r^2-side\times side$

$=2\times \frac{90}{360}\times \frac{22}{7}\times 8\times 8-8\times 8$

$=\frac{2\times 352}{7}-64=\frac{704-448}{7}=\frac{256}{7}{cm}^2$