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Question

Adjoining figure two arcs PAQ and PBQ is a part of a circle with center O and radius OP while arcs PBQ is a semicircle drawn on PQ as diameter, If OP=PQ=10 cm. Show that the area of the shaded region is 25(3π6)cm2
1380313_4f45c39a8f7f4dab8117525e0fb6ac3d.png

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Solution

Since OP=PQ=QO
POQ is an equilateral triangle.
POQ=60
Area of segment PAQM
=θ360πr234a2
=60360π×10234102
=(100π610034)cm2
Area of semicircle with M as centre is π2×52=25π2cm2
Area of shaded region=25π2(50π3253)
=25π250π3+253
=25π6+253
=25(3π6)cm2

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