Question

If diagonal of a square is $8cm$, then its area is

• A. $4c{m}^2$
• B. $16c{m}^2$
• C. $24c{m}^2$
• D. $32c{m}^2$

Answer 1

The correct option is D $32c{m}^2$

Here, $ABCD$ is a square.

Let $AB=BC=CD=AD=a$ [ All sides of square are equal ]

$\Rightarrow$ $AC=8cm$ [ Given ]

In right angled $△ABC$,

$\Rightarrow$ $(AC{)}^2=(AB{)}^2+(BC{)}^2$ [ By Pythagoras theorem ]

$\Rightarrow$ $(8{)}^2=a^2+a^2$

$\Rightarrow$ $64=2a^2$

$\Rightarrow$ $a^2=32$

$\Rightarrow$ Area of a square $=a^2=32c{m}^2$