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Question
ABCD is a given rectangle with length as 80 cm and breadth as 60 cm. P, Q, R, S are the midpoints of sides AB, BC, CD, DA respectively. A circular rangoli of radius 10 cm is drawn at the centre as shown in the following figure. Find the area of shaded portion.
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Solution
Here, AP = `1/2` AB = `1/2 xx 80` = 40 cm
Also, AS = `1/2` AD = `1/2 xx 60` = 30 cm
Area of ΔAPS = `1/2` × AP × AS = `1/2` × 40 × 30 = 600 cm2
Area of portion PQRS = Area of rectangle ABCD – 4 × Area of ΔAPS
= 80 × 60 – 4 × 600
= 4800 – 2400
= 2400 cm2
Area of circular rangoli = π × (10)2 ...[∵ Radius of circle = 10 cm]
= `22/7 xx 100`
= 314 cm2
∴ Area of shaded region = 2400 – 314 = 2086 cm2
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