Question

Find the area of the shaded region .

Answer 1

Calculate area of the white region inside circle.

Area of the two white triangles in top left and bottom right:

$2 \cdot \frac{1}{2}(6)(6) = 36 ft^2$

Area of the two white quarter circles in the bottom left and top right:

$2 \cdot \frac{1}{4}\pi (6)^2 = 18\pi ft^2$

Total area of unshaded white region inside circle:

$(36 + 18\pi)ft^2$

Area of entire circle including the white and shaded regions

$\pi(6)^2 = 36\pi ft^2$

Area of shaded region is area of entire circle - area of unshaded white region

$36\pi - (36 + 18\pi) = (18\pi - 36) ft^2$