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In figure , ABCD is a square of side 14 cm. With centres 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.


Answer :


The area of the whole square ABCD \( = \ 14^2 \ = \ 196 \)cm2

The sum of the area of the four quadrants at the four corners of the square

= The area of a circle of radius 7cm

\(= \ \pi(7)^2 \ = \ \frac{22}{7} \ × \ 49 \ = \ 154 \) cm2

Area of the shaded portion = The area of the square ABCD - The sum of the area of four quadrants at the four corners of the square

\(= \ 196 \ - \ 154 \ = \ 42 \) cm2

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