CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

In the fig., $$OABC$$ is a square inscribed in a quadrant $$OPBQ$$. If $$OA=20$$cm, Find the area of shaded region. $$\left [  \pi =3.14 \right ]$$     
1365937_2941f83b541f4d2d88e63a9ff70563dd.PNG


Solution

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 = $$208 cm^{2}$$
Hence area of shaded region is $$208 cm^{2}$$

1188670_1365937_ans_8262152f54734c248393bd32f7479e93.JPG

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image