Question

In Fig., a square $OABC$ is inscribed in a quadrant $OPBQ$. If $OA=20cm$, find the area of the shaded region. (Use $\pi =3.14$)

Answer 1

From given figure

$OB=$ Diagonal of $\square ABCO$ $=$ Radius of quadrant QOP
$\therefore$ $OB=OA\times \sqrt{2}$ $=20\sqrt{2}cm$
$\therefore$ Area of $\square OABC=20\times 20=400c{m}^2$
Area of quadrant QOP$=\frac{\pi \times r^2}{4}$

$=\frac{1}{4}\times 3.14\times (20\sqrt{2}{)}^2$

$=628c{m}^2$
$\therefore$ Area of shaded region $=628-400=228c{m}^2$