Question

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

Solution

## REF.ImageIn Given figureOABC is a square.OA= 20 cmIn $$\Delta OAB$$$$OB=\sqrt{(OA)^{2}+(AB)^{2}}$$$$OB=\sqrt{(20)^{2}+(20)^{2}}[OA=AB]$$$$OB=20\sqrt{2} cm$$Hence radius of quadrant is $$20\sqrt{2} cm$$nowarea of shaded region = area of quadrant - ar of squareArea = $$\frac{\pi r^{2}}{4}-(OA)^{2}$$Area = $$\frac{3.14\times (20\sqrt{2})^{2}}{4}-(20)^{2}=(20)^{2}[\frac{3.14}{2}-1]$$Area = $$208 cm^{2}$$Hence area of shaded region is $$208 cm^{2}$$Mathematics

Suggest Corrections

0

Similar questions
View More

People also searched for
View More