A rhombus has perimeter $40$ cm and one diagonal of $12$ cm. Find its area.
A rhombus has perimeter $40$ cm and one diagonal of $12$ cm. Find its area.
$96 \text{ cm}^{2}$
$120 \text{ cm}^{2}$
$48 \text{ cm}^{2}$
$60 \text{ cm}^{2}$
Solution
Side $= 40/4 = 10$ cm. Half of given diagonal $= 6$. Half of other diagonal $= \sqrt{10^{2}-6^{2}} = 8$, so other diagonal $= 16$. Area $= \dfrac{1}{2}\times 12 \times 16 = 96 \text{ cm}^{2}$.