Question:
The length of the diagonal of a square is $10 \sqrt{2} \mathrm{~cm}$. Its area is
(a) 200 cm2
(b) 100 cm2
(c) 150 cm2
(d) $100 \sqrt{2} \mathrm{~cm}^{2}$
Solution:
(b) 100 cm2
A diagonal of a square forms the hypotenuse of a right-angled triangle with base and height equal to side a.
Diagonal $^{2}=a^{2}+a^{2}$
$\Rightarrow$ Diagonal $^{2}=2 a^{2}$
$\Rightarrow a=\frac{1}{\sqrt{2}}$ Diagonal
$=\frac{1}{\sqrt{2}} \times 10 \sqrt{2}$
$=10 \mathrm{~cm}$
$\therefore$ Area of the square $=a^{2}=10 \times 10=100 \mathrm{~cm}^{2}$