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.
Solution:
Area of the rhombus $=\frac{1}{2} \times d_{1 \times} d_{2}$, where $d_{1}$ and $d_{2}$ are the lengths of the diagonals.
$=\frac{1}{2} \times 30 \times 16$
$=240 \mathrm{~cm}^{2}$
Side of the rhombus $=\frac{1}{2} \sqrt{{d_{1}}^{2}+{d_{2}}^{2}}$
$=\frac{1}{2} \sqrt{30^{2}+16^{2}}$
$=\frac{1}{2} \sqrt{1156}$
$=\frac{1}{2} \times 34$
$=17 \mathrm{~cm}$
Perimeter of the rhombus $=4 a$
$=4 \times 17$
= 68 cm
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