Question

The given figure shows a rectangle ABC 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. 374.5 $c{m}^2$
• B. 374.5 $m^2$
• C. 3.745 $c{m}^2$
• D. 37.45 $c{m}^2$

Answer 1

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

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 $△ABC$
$A{C}^2=A{B}^2+C{B}^2$
$={28}^2+{21}^2$
$=784+441$
$=1225$
$=>A{C}^2=\sqrt{1225}$
$=>AC=35cm$
$\therefore$ 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
=$962.5-588c{m}^2$
=$374.5c{m}^2$