Each side of a rhombus is $13$ cm and one diagonal is $10$ cm. Find the area of the rhombus.
Each side of a rhombus is $13$ cm and one diagonal is $10$ cm. Find the area of the rhombus.
$60 \text{ cm}^{2}$
$120 \text{ cm}^{2}$
$130 \text{ cm}^{2}$
$169 \text{ cm}^{2}$
Solution
Diagonals of a rhombus bisect each other at right angles. Half of the known diagonal $= 5$ cm. Half of the other diagonal $= \sqrt{13^{2}-5^{2}} = \sqrt{144} = 12$ cm, so the other diagonal $= 24$ cm. Area $= \dfrac{1}{2}\times 10 \times 24 = 120 \text{ cm}^{2}$.