In the given figure, a square ABCD is inscribed in a quadrant APCQ. If AB = 16 cm, find the area of the shaded region (take π = 3.14) correct to two places of decimal.

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 02 Dec 2022 Shift 4)

Answer 1

Given:

AB = 16 cm

Concept used:

Area of a square = a²

Area of a quadrant of a circle = πr²/4

The diagonal of a square = a√2

Here,

a = side of the square

r = radius of the circle

Calculation:

F1 SSC Amit A 24-02-2023 D14

Here

AC is the diagonal of the square ABCD and also the radius of the quadrant APCQ

Now,

AC = 16√2

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

⇒ Area of the shaded region = π × (16√2)²/4 - 16²

⇒ Area of the shaded region = 3.14 × 128 - 256

⇒ Area of the shaded region = 401.92 - 256

⇒ Area of the shaded region = 145.92 cm²

∴ The area of the shaded region is 145.92 cm2.

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