Mathematics
In the given figure, ABCD is a square of side 7 cm and A, B, C, D are centres of equal circles which touch externally in pairs. Find the area of the shaded region.
Mensuration
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Answer
Given,
ABCD is a square.
Side = 7 cm
Distance between centres of each circle = 7 cm
2r = 7
r = = 3.5 cm.
Area of 4 circles:
Area of one circle = πr2
= × (3.5)2
= × 12.25
= 22 × 1.75 = 38.5
∴ For 4 circles, area = 4 × 38.5 = 154 cm2.
Area of square :
(side)2 = 72 = 49 cm2.
Area of 4 quadrants = Area of one circle = 38.5 cm2.
Area of shaded region = Area of square + Area of 4 circle - Area of 4 quadrants
= 49 + 154 - 38.5
= 164.5 cm2.
Hence, area of shaded region = 164.5 cm2.
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