Question

Each diagonal of a square is $12cm$ long. Its area is
(a) $144c{m}^2$
(b) $72c{m}^2$
(c) $36c{m}^2$
(d) none of these

Answer 1

(b) $72c{m}^2$
Let the side of the square be ${}^{\prime }{a}^{\prime }$ units

Diagonal of a square $=\sqrt{2}a=12$

$\therefore a=\frac{12}{\sqrt{2}}=6\sqrt{2}$ cm

Thus, area of the square $=a^2=6\sqrt{2}\times 6\sqrt{2}=72c{m}^2$