In the figure 7.44, O is the centre of the circle. m(arc PQR) = 60°, OP = 10 cm. Find the area of the shaded region. ( π=3.14,\ sqrt3=1.73 ) Figure: P and R are on the circle, Q on the minor arc PR; the shaded region is the minor segment between chord PR and arc PQR.

O is the centre of the circle. m(arc PQR) = 60°, OP = 10 cm. Find the area of the shaded region (minor segment PQR). (π = 3.14, √3 = 1.73)

In the figure 7.44, O is the centre of the circle. m(arc PQR) = 60°, OP = 10 cm. Find the area of the shaded region. (\(\pi=3.14,\ \sqrt3=1.73\))

Figure: P and R are on the circle, Q on the minor arc PR; the shaded region is the minor segment between chord PR and arc PQR.

Doubtly Asked 24 Oct 2026 Save WhatsApp Report

Answer: ≈ 9.08 cm²

\(\angle POR=60^\circ\) and OP = OR, so ΔPOR is equilateral with side 10 cm.

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

\[A(\text{sector})=\frac{60}{360}\times3.14\times100=52.33\]

\[A(\Delta POR)=\frac{\sqrt3}{4}\times100=25\times1.73=43.25\]

\[A(\text{shaded})=52.33-43.25=9.08\ \text{cm}^2\]

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

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