Question

The area of a square $ABCD$ is $64sq.cm$. Find the area of square obtained by joining the mid-points of the sides of the square $ABCD$.

Answer 1

$ar\left[ABCD\right]=64$

$s^2=64$

$s=8$

'$s$' is length of side of square $ABCD$

$EFGH$ is the square

obtained by joining mid pts

of $ABCD$

side of square $EFGH=\left(\frac{5}{2}\right)\sqrt{2}$

$=\frac{5}{\sqrt{2}}$

$\therefore$ Area of $EFGH={\left(\frac{5}{\sqrt{2}}\right)}^2=\frac{s^2}{2}=\frac{64}{2}=32sq.units.$