Find the area of the rhombus, the lengths of whose diagonals are 30 cm

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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