Question

The given figure shows a rectangle $ABCD$ inscribed in a circle as shown alongside.
If $AB=28$ cm and $BC=21$ cm, find the area of the shaded portion of the given figure.

• A. $374.5c{m}^2$
• B. $274.5c{m}^2$
• C. $174.5c{m}^2$
• D. None of these

Answer 1

The correct option is A $374.5c{m}^2$

Diagonal $AC$ passes through the centre of the circle.
$\therefore$ $AC$ is the diameter.
Now, area of rectangle $ABCD=$ $AB\times AC$
$=$ $28\times 21$
$=$ $588c{m}^2$
In $△ABC$
$A{C}^2=A{B}^2+C{B}^2$
$={28}^2+{21}^2$
$=784+441$
$=1225$
$\Rightarrow A{C}^2=\sqrt{1225}$
$\Rightarrow AC=35$ cm
$\therefore$ radius $=$ $\frac{AC}{2}$
$=$ $\frac{35}{2}$
$=$ $17.5$
Area of the circle $=$ $\pi r^2$
$=$ $\frac{22}{7}\times (17.5{)}^2$
$=$ $962.5c{m}^2$
Area of the shaded region $=$ Area of the circle $-$ Area of rectangle $ABCD$
$=$ $962.5-588c{m}^2$
$=$ $374.5c{m}^2$