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Question 127

ABCD is a given rectangle with length as 80 cm and breadth as 60 cm. P, Q, R, S are the mid-points 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 =12 AB =12×80=40 cm

Also, AS =12 AD =12×60=30 cm

Area of ΔAPS=12×AP×AS=12×40×30=600 cm2

Area of portion PQRS = Area of rectangle ABCD - 4 × Area of ΔAPS=80×604×600

=48002400=2400 cm2

Area of circular rangoli =π×(10)2=227×100=314 cm2 [ radius of circle = 10 cm]

Area of shaded region = 2400 - 314 = 2086 cm2


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