Question

In the fig., $OABC$ is a square inscribed in a quadrant $OPBQ$. If $OA=20$cm, Find the area of shaded region. $[\pi =3.14]$

Answer 1

REF.Image

In Given figure

OABC is a square.

OA= 20 cm

In $\Delta OAB$

$OB=\sqrt{(OA{)}^2+(AB{)}^2}$

$OB=\sqrt{(20{)}^2+(20{)}^2}[OA=AB]$

$OB=20\sqrt{2}cm$

Hence radius of quadrant is $20\sqrt{2}cm$

now

area of shaded region = area of quadrant - ar of square

Area = $\frac{\pi r^2}{4}-(OA{)}^2$

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

Area = $208c{m}^2$

Hence area of shaded region is $208c{m}^2$