Question

In the given figure, $ABCD$ is a square of side $5cm$ inscribed in a circle. Find the area of the shaded region
[Take $\pi =3.14$]

• A. $14.25c{m}^2$
• B. $16.75c{m}^2$
• C. $25c{m}^2$
• D. $15.25c{m}^2$

Answer 1

Answer: (A)

$14.25c{m}^2$

Diagonal $AC$ is the diameter of the circle with centre $O$
$\therefore OC=OA=$ radius of the circle.

Given,
$AB=AC=5cm$
$△ABC$ is a right-angled triangle.
$\therefore A{C}^2=A{B}^2+A{C}^2$
$=5^2+5^2$
$=25+25$
$=50cm$
$\Rightarrow AC=5\sqrt{2}$

$\therefore OA=OC=\frac{AC}{2}$
Radius $=\frac{5\sqrt{2}}{2}$

Area of square $=A{C}^2$
$=5^2$
$=25$

Area of circle $=\pi r^2$
$=3.14\times {\left(\frac{5\sqrt{2}}{2}\right)}^2$
$=3.14\times \frac{50}{4}$
$=39.25$

$\therefore$Area of the shaded region $=$ Area of circle $-$ Area of square
$=39.25-25$
$=14.25c{m}^2$