Question

# Find the area of a rhombus whose side is 5cm and whose altitude is 4.8cm. If one of its diagonals is 8cm long, find the length of the other diagonal.

Area of the rhombus = Base $\times$ Height = $\frac{1}{2} \times$Product of diagonals
$\Rightarrow 5 \times 4.8 = \frac{1}{2} \times (8 \times x)$
$\Rightarrow 24 = \frac{1}{2} \times (8 \times x)$
$\Rightarrow x = 6cm$
Note: In rhombus all sides are equal, so the base is as same as its side. The altitude (height) of a rhombus is the perpendicular distance from the base to the opposite side. The diagonal of a rhombus divides it into two congruent triangles. Since the diagonals of a rhombus bisect each other at $90^\circ$ , we can calculate the height and the base of one of these triangles and multiply the result by two to get the area of the rhombus.