A figure consists of a square of side 'a' m w | vedclass

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(D) The total area is the sum of the area of the square and the areas of the four semi-circles.Area of the square $= a^{2}$.Each side of the square ac

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$a^{2} + \frac{\pi a^{2}}{2}$

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(D) The total area is the sum of the area of the square and the areas of the four semi-circles.Area of the square $= a^{2}$.Each side of the square acts as the diameter of a semi-circle,so the radius $r = \frac{a}{2}$.Area of one semi-circle $= \frac{1}{2} \pi r^{2} = \frac{1}{2} \pi (\frac{a}{2})^{2} = \frac{\pi a^{2}}{8}$.Since there are four such semi-circles,the total area of the four semi-circles $= 4 	imes \frac{\pi a^{2}}{8} = \frac{\pi a^{2}}{2}$.Therefore,the total area of the figure $= a^{2} + \frac{\pi a^{2}}{2}$.

$A$ figure consists of a square of side '$a$' $m$ with semi-circles drawn on the outside of the square. The area (in $m^{2}$) of the figure so formed will be

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