Question

If the diagonal of a square is $12cm,$ then the area of the square is

• A. $144{cm}^2$
• B. $48{cm}^2$
• C. $72{cm}^2$
• D. $100{cm}^2$

Answer 1

The correct option is C $72{cm}^2$

Given$\Rightarrow$

Diagonal $=12cm$

In $\Delta ABD\Rightarrow A{D}^2=A{B}^2+B{D}^2$ ....... Pythagoras theorem

$2A{B}^2=A{D}^2\Rightarrow 144=2A{B}^2$ ...... $AB=BD$

$AB=\sqrt{\frac{144}{2}}=\frac{12}{\sqrt{2}}cm$

Area of square $=sid{e}^2=(AB{)}^2=\frac{144}{2}c{m}^2=72c{m}^2$