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

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answer is A.

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Detailed Solution

Given that a square OABC is inscribed in a quadrant OPBQ.
In Fig. 12.31, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region.

In Fig. 12.31, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region.

From the given figure, triangle OAB is a right angled triangle.
Using Pythagoras theorem.

⇒ OB 2 =OA 2 +A 2

→ (1)

⇒ OA=20 c m

,
Let

AB=20 c m

(Since it is a square, all sides are equal in length)
Substitute OA & AB in Eq (1).

⇒ OB 2 = 202 + 202

⇒ OB 2 =2 202

⇒ OB= 2202

Radius of the quadrant is

.
Area of a quadrant

= π r 2 4

Area of a quadrant OQBP

= π 2022 4

⇒ A r e a = 3.14 2022 4

⇒ A r e a = 3.14 800 4

⇒ A r e a = 25124

Area of a quadrant OQBP

→ (1)

Area of square

= a 2

⇒ A r e a o f s q u a r e = 202

→ (2)

Area of the shaded region = Area of quadrant OQBP – Area of square OABC
Substitute Eq (1) & Eq (2) in the above equation.
Area of the shaded region
Question Image

Hence, the area of the shaded region is

.
Therefore the answer is option (1).

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