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.

Answer 1

Hint: Here, we will use the formula for finding the area of rhombus to get the required solution.
Area of the rhombus = Base $ \times $ Height = $\frac{1}{2} \times $Product of diagonals
It is given that the side of the rhombus is 5cm and altitude is 4.8 cm and one diagonal length is 8cm.
Let the second diagonal length of the given rhombus be x.
Substituting these given values in the formula of area of rhombus,
$ \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.