Physics

In figure, $$A,B,C,D$$ are centre of equal circles which touch externally in pairs and $$ABCD$$ is a square of side $$7cm$$. Find the area of the shaded region.


SOLUTION
Area of square ABCD $$=7^2$$
                                     $$=49\ cm^2$$
Radius $$=\dfrac{Side\ of\ square}{2}$$
            $$=\dfrac{7}{2}\ cm$$
Area of 4 quadrant $$=4\times\dfrac{1}{4}\pi r^2$$
                                $$=4\times\dfrac{1}{4}\times\dfrac{22}{7}\times\dfrac{7}{2}\times\dfrac{7}{2}$$
                                $$=\dfrac{77}{2}\ cm^2$$
Area o shaded region $$=49-\dfrac{77}{2}$$
                                      $$=\dfrac{98-77}{2}$$
                                       $$=\dfrac{21}{2}\ cm^2$$
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