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]$latex \frac{a^{2}}{4}&s=1$
[B]$latex \frac{a}{\sqrt{2}}&s=1$
[C]2a
[D]$latex \frac{a^{2}}{2}&s=1$
$latex \frac{a^{2}}{2}&s=1$
$latex Side = \frac{Diagonal}{\sqrt{2}}&s=1$ $latex = \frac{a}{\sqrt{2}}&s=1$
$latex \therefore Area = (Side)^{2}&s=1$
$latex = \left ( \frac{a}{\sqrt{2}} \right )^{2} sq.cm = \frac{a^{2}}{2} sq.cm&s=1$
Hence option [D] is the right answer.