Question

in the given figure OABC is a square and OPBQ is a quadrant of a circle if OA= 20 CM then find the area of the shaded region​

Answer 1

Answer:

Area of shaded region is 228.6 square centimeter.

Step-by-step explanation:

Given OABC is a square and OPBQ is a quadrant of a circle if OA= 20 cm.

We have to find the area of shaded region.

ar(shaded region)=ar(quadrant)-ar(square)

Side of square=OA=20 cm=AB

$\text{Area of square=}side\times side=20\times 20=400 cm^2$

Radius of quadrant=OB

By Pythagoras theorem

$OB^2=OA^2+AB^2=20^2+20^2=800$

⇒ $OB=\sqrt{800}=20\sqrt2cm$

$\text{Area of quadrant=}\frac{\pi r^2}{4}$

                           =$\frac{800\times 22}{4\times 7}$

                            =$\frac{4400}{7}cm^2$

ar(shaded region)=ar(quadrant)-ar(square)

                              =$\frac{4400}{7}-400 cm^2$

                              =$\frac{1600}{7}cm^2=228.6 cm^2$

         

Answer 2

Answer:

85.72

area of the shaded region = area of the sector - area of the square