Question

In the given figure, a square OABC is inscribed in a quadrant OPBQ. If OA = 15cm, find the area of the shaded region. [Use π = 3.14]​

Answer 1

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Answer 2

Solution:-

In Δ OAB,

OB² = OA² + AB²

OB² = 15² + 15²

OB² = 225 + 225

OB² = 450

OB = √450

OB = 21.21 cm

Now, OB = 21.21 cm is the radius of the circle.

Area of quadrant = 90°/360° × 3.14× (21.21)²

= 1/4 × 3.14× 450

= 353.24 cm^2

Area of the quadrant = 353.25 sq cm

Now, area of the square OABC = 15 × 15

= 225 sq cm

area of shaded region = area of quadrant - area of square

= 353.25 - 225

Area of shaded region = 128.25

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@GauravSaxena01