Question

In a square abcd the shaded region is the v intersection of two circular regions centered at b and
d. if ab =10 then what is v the area v of v shaded region

Answer 1

Refer to the attached image.

As, we can observe clearly from the image that

Area of square = Area of 2 quadrants - Area of common shaded region

$(side)^2 = 2 \times \frac{1}{4} (\pi r^2)$ - Area of common shaded region

Therefore, Area of common shaded region

= $2 \times \frac{1}{4} (\pi r^2)-(side)^2$

= $2 \times \frac{1}{4} \pi (10)^2 - (10)^2$

= $\frac{1}{2} \pi (10)^2 - (10)^2$

= $50 \pi - 100$

= $50(\pi-2)$

Therefore, the area of shaded region is  $50(\pi-2)$ square units.