Question

The area of the shaded region

• A. $29c{m}^2$
• B. $30.5c{m}^2$
• C. $25c{m}^2$
• D. $32.5c{m}^2$

Answer 1

Answer: (B)

$30.5c{m}^2$

Given,
$AB=8$ cm and $BC=6$ cm
The diagonal of the inscribed rectangle will be the diameter of the circle.
Thus, by Pythagoras Theorem, we get
$(AC{)}^2=(AB{)}^2+(AC{)}^2$
$=8^2+6^2$
$=64+36$
$=100$
$=>AC=\sqrt{100}$
$=>AC=10$
Thus, radius $=\frac{10}{2}$
$=5$ cm
Area of the rectangle ABCD $=8\times 6$
$=48c{m}^2$
Area of the circle $=\pi (5{)}^2$
$=3.14\times 25$
$=78.5c{m}^2$
Thus, the area of the shaded portion is $=(78.5-48)c{m}^2$
$=30.5c{m}^2$