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Offline Centres

In figure, ABCD is a square of side 14 cm. With centers A, B, C and D, four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of the shaded region.

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52 {cm}^{2}

62 {cm}^{2}

72 {cm}^{2}

42 {cm}^{2}

answer is D.

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Detailed Solution

Given,
Square ABCD side = 14 cm
This side is equal to diameter of circle.
So, Radius of circles = 14/2 cm = 7 cm
Area of square ABCD,

A_{s} = (Side)^{2}

A_{s} = (14)^{2}

A_{s} = 196 {cm}^{2}

Area of 4 sector with 7 cm radius,
Area of 4 sectors

= 4 \times \frac{π r^{2}}{4}

Area of 4 sectors

= \frac{22}{7} \times 7 \times 7

Area of 4 sectors

= 154 {cm}^{2}

Now, from the figure
Shaded region area
= square area- four sectors subtending right angle area
= Area of square ABCD - 4 × Area of sectors

= 196 {cm}^{2} - 154 {cm}^{2}

= 42 {cm}^{2}

Thus, area of shaded portion =

42 {cm}^{2}

Correct option is 4.

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