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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Question

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.

KnowledgeBoat · Accepted 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.

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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