Find the area of a rhombus whose side is 6 cm and whose altitude is 4 cm.

Question:

Find the area of a rhombus whose side is 6 cm and whose altitude is 4 cm. If one of its diagonals is 8 cm long, find the length of the other diagonal.

Solution:

Given:

Side of the rhombus $=6 \mathrm{~cm}$

Altitude $=4 \mathrm{~cm}$

One of the diagonals $=8 \mathrm{~cm}$

Area of the rhombus $=$ Side $\times$ Altitude $=6 \times 4=24 \mathrm{~cm}^{2} \quad \ldots \ldots \ldots$ (i)

We know : Area of rhombus $=\frac{1}{2} \times \mathrm{d}_{1} \times \mathrm{d}_{2}$

Using (i):

$24=\frac{1}{2} \times \mathrm{d}_{1} \times \mathrm{d}_{2}$

$24=\frac{1}{2} \times 8 \times \mathrm{d}_{2}$

$\mathrm{~d}_{2}=6 \mathrm{~cm}$

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