Q. The length of the diagonal of a square is 'a' cm. Which of the following represents the area of the square (in sq.cm) ?
Answer: $latex \frac{a^{2}}{2}&s=1$
Notes: $latex Side = \frac{Diagonal}{\sqrt{2}}&s=1$ $latex = \frac{a}{\sqrt{2}}&s=1$ $latex \therefore Area = (Side)^{2}&s=1$ $latex = \left ( \frac{a}{\sqrt{2}} \right )^{2} sq.cm = \frac{a^{2}}{2} sq.cm&s=1$ Hence option [D] is the right answer.

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