Question

Rectangle $ABCD$ is inscribed in the circle as shown in the above figure. If the length of side $AB$ is $5$ and the length of side $BC$ is $12$, calculate the area of the shaded region.

• A. $40.8$
• B. $53.1$
• C. $72.7$
• D. $78.5$
• E. $81.7$

Answer 1

The correct option is C $72.7$

Since the rectangle is inscribed, then diagonal of the rectangle is equal to the diameter of the circle.

Given: $AB=5,BC=12$

Diagonal of rectangle $=$ $\sqrt{5^2+{12}^2}$

Diagonal $=$ $\sqrt{25+144}=13$

Shaded region is area of circle $-$ area of rectangle $=$ $\frac{\pi \times 169}{4}-60=72.73$