Question 40

The length of each of the sides of a rhombus is given as 5 m and the length of one of its diagonals is 2.8 m. Find the area of the rhombus.

Solution

The length of each of the sides of a rhombus is given as 5 m and the length of one of its diagonals is 2.8 m.

So AB=5cm, AC=1.4cm

In triangle ABC,

Acc Pythagoras theorem,

$$AB^2=BC^2+AC^2$$

$$BC^2={5}^2-{1.4}^2$$

$$BC=\sqrt{25-1.96}$$

$$BC=\sqrt{23.04} = 4.8 cm$$

So two diagonals are 2.8cm and 9.6 cm

$$Area = \frac{1}{2}\times 9.6\times 2.8$$

$$=13.44cm^2$$

Option B is correct.

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