In the figure 7.45, if A is the centre of the circle. ∠PAR = 30°, AP = 7.5, find the area of the segment PQR. ( π=3.14 ) Figure: P and R are on the circle, Q on the minor arc PR; segment PQR is the minor segment cut off by chord PR.

Answer: 0.65625 sq. unit Area of segment = area of sector − area of triangle formed by the two radii and the chord. A(sector)=30/360×3.14×7.5²=14.71875 A(Δ PAR)=1/2r²sinθ=1/2×56.25×1/2=14.0625 A(segment)=14.71875-14.0625=0.65625

A is the centre of the circle. ∠PAR = 30°, AP = 7.5, find the area of the segment PQR. (π = 3.14)

In the figure 7.45, if A is the centre of the circle. ∠PAR = 30°, AP = 7.5, find the area of the segment PQR. (\(\pi=3.14\))

Figure: P and R are on the circle, Q on the minor arc PR; segment PQR is the minor segment cut off by chord PR.

Doubtly Asked 24 Oct 2026 Save WhatsApp Report

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Answer: 0.65625 sq. unit

Area of segment = area of sector − area of triangle formed by the two radii and the chord.

\[A(\text{sector})=\frac{30}{360}\times3.14\times7.5^2=14.71875\]

\[A(\Delta PAR)=\tfrac12r^2\sin\theta=\tfrac12\times56.25\times\tfrac12=14.0625\]

\[A(\text{segment})=14.71875-14.0625=0.65625\]

Doubtly AI · 24 Oct 2026 AI-verified · Oct 2026 Report

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A is the centre of the circle. ∠PAR = 30°, AP = 7.5, find the area of the segment PQR. (π = 3.14)

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