In the given figure, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region.

Asked by Pragya Singh | 1 year ago |  158

#### 1 Answer

##### Solution :-

Side of square = OA = AB = 20 cm

Radius of the quadrant = OB

OAB is right angled triangle

By Pythagoras theorem in ΔOAB,

OB= AB2+OA2

⇒ OB= 20+202

⇒ OB= 400+400

⇒ OB= 800

⇒ OB= $$20 \sqrt{2}$$ cm

Area of the quadrant = $$\dfrac{πR^2}{4}$$ cm

=$$\dfrac{3.14}{4}×(20\sqrt{2})^2$$  cm= 628cm2

Area of the square = 20×20 = 400 cm2

Area of the shaded region = Area of the quadrant – Area of the square

= 628-400 cm= 228cm2

Answered by Abhisek | 1 year ago

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