Question

The perimeter of a rhombus is 40 cm. If one diagonal is 16 cm, find its area in cm${}^2$

Answer 1

Perimeter= 4$\times$L

40= 4$\times$L

$L=10$ cm

$\Rightarrow$L${}^2$=($\frac{d_1}{2}$)${}^2$+($\frac{d_2}{2}$)${}^2$

10${}^2$=8${}^2$+($\frac{d_2}{2}$)${}^2$

$d_2=12$ cm

Area = $\frac{1}{2}(d_1\times d_2)$

= $\frac{1}{2}$(16$\times$12)

= 96 $c{m}^2$.