Question

In the following figure, the area of the segment PAQ is
(a)$\frac{a^{2}}{4}(\pi+2)$
(b)$\frac{a^{2}}{4}(\pi-2)$
(c)$\frac{a^{2}}{4}(\pi-1)$
(d)$\frac{a^{2}}{4}(\pi+1)$​

Answer 1

Answer:

The area of the segment, PAQ is a²/4(π - 2) .

Among the given options option (b) a²/4(π - 2)  is the correct answer.

Step-by-step explanation:

Given :

Radius of a circle,r = a  

Angle at the centre of a circle, θ = 90°

Area of the segment PAQ ,A = {πθ/360 - sin θ /2 cos θ/2 }r²

A = {90°π/360° - sin 90°/2 cos 90°/2 }× a²

A = {π/4  - sin 45°cos 45°} × a²

A = {π/4  - 1/√2 × 1/√2} × a²

A = {π/4  - 1/2 } × a²

A = {(π/4 - 1× 2)/4}a²

A = {(π - 2)/4}a²

A = a²/4(π - 2)  

Area of the segment, PAQ = a²/4(π - 2)  

Hence, the area of the segment, PAQ is a²/4(π - 2) .

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Answer 2

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