Question

ABCD is a given rectangle with length as 80 cm and breadth as 60cm. P, Q, R and S are the mid-points of sides AB, BC, CD and 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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Answer 1

Answer:

Let P,Q,R,S be the mid points of sides AB,BC,CD,DA respectively.

AP= 1/2 AB

40= 1/2 x 80

AS= 1/2 AD

60 = 1/2 x 30

Now, 1/2 AP = AS = 1/2 x 40 x 30 = 600 cm²

Since, P,Q,R,S are the mid points of sides AB,BC,CD,DA respectively, APS,RDS,RCQ,PBQ are congruent triangles.

PQRS = ABCD - 4 x ABC

=80×60−4×600

=4800−2400

=2400cm²

Circular rangoli has radius r=10 cm

Area of circular rangoli,

=πr²

=π×(10)²

=3.14×100

=314cm²

area of shaded portion=Area of PQRS - Area of circular rangoli

=2400−314=2086cm²

Thus, Area of shaded portion is 2086cm².