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The length of the diagonal of a square is ‘a’ cm. Which of the following represents the area of the square (in sq.cm) ?

The length of the diagonal of a square is ‘a’ cm. Which of the following represents the area of the square (in sq.cm) ?
[A]\frac{a^{2}}{4}
[B]\frac{a}{\sqrt{2}}
[C]2a
[D]\frac{a^{2}}{2}

\frac{a^{2}}{2}
Side = \frac{Diagonal}{\sqrt{2}} = \frac{a}{\sqrt{2}}
\therefore Area = (Side)^{2}
= \left ( \frac{a}{\sqrt{2}} \right )^{2} sq.cm = \frac{a^{2}}{2} sq.cm
Hence option [D] is the right answer.

Originally written on June 14, 2016 and last modified on June 29, 2016.
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