Question

Find the area of the rhombus, the lengths of whose diagonals are 30 cm and 16 cm. Also find the perimeter of the rhombus.

Answer 1

Area of the rhombus = $\frac{1}{2}\times d_{1\times }{d}_2$, where d₁ and d₂ are the lengths of the diagonals.

$$\begin{gathered} =\frac{1}{2}\times 30\times 16 \\ =240{\mathrm{cm}}^2 \end{gathered}$$

Side of the rhombus = $\frac{1}{2}\sqrt{{d_1}^2+{d_2}^2}$

$$\begin{gathered} =\frac{1}{2}\sqrt{{30}^2+{16}^2} \\ =\frac{1}{2}\sqrt{1156} \\ =\frac{1}{2}\times 34 \\ =17\mathrm{cm} \end{gathered}$$

Perimeter of the rhombus = $4a$
= $4\times 17$
= 68 cm