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

In Fig., a square OABC is inscribed in a quadrant OPBQ . If OA = 20 cm ,  find the area of the shaded region. (Use pi = 3.14 )

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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