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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 given 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 × 60 = 600 cm^{2}

Area of portion PQRS = Area of rectangle ABCD – 4 × Area of ΔAPS

= 80 × 60 – 4 × 600

= 4800 – 2400

= 2400 cm^{2 }

Area of circular rangoli = π × (10)^{2} ......[∵ Radius of circle = 10 cm]

= `22/7 xx 100`

= 314 cm^{2}

∴ Area of shaded region = 2400 – 314 = 2086 cm^{2}

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