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Question

Find the area of the shaded portion as shown in the adjoining figure. The four corners are quadrants of circle and at the centre there is a circle.
1125696_39dfe25062c946a3b2154ab83d42dc9d.png

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Solution

Let the center of circle be at O. AC is diagonal of square ABCD

AC=42cm

we have AE=CF=1cm each

EF=ACAECF

EF=422

radius of circle =12EF=12(422)=221

Area of shaded region = area (ABCD) (area of circle + 4× area of each quadrant)

=4×4[π×(221)2+4×14π(1)2]

=16π{(221)2+1}

=16π{8+142+1}

=16(1042)π

=1613.64439 (Taking 2=1.414,π=3.14)

Area =2.36cm2

1346689_1125696_ans_104a7185863e4fbeaecd9e0e7a2a0e3a.png

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