# Ex.11.2 Q5 Mensuration Solution - NCERT Maths Class 8

## Question

The diagonals of a rhombus are \(7.5\,\rm{ cm}\) and \(12\,\rm{ cm.}\) Find its area.

## Text Solution

**What is Known?**

Diagonals of the rhombus are given.

**What is unknown?**

Area of rhombus.

**Reasoning:**

By using the method of splitting into triangles (triangulation method) we can find area of the rhombus visually diagonals \(AD\) and \(BC\) are perpendicular bisectors of each other hence area of rhombus \(ABCD\) will be the sum of area of triangle \(ACB\) and area of the triangle \(DBC. \)

**Steps:**

Area of Rhombus \(ABCD\)

\[\begin{align} &= {\text{Area of }}\Delta \,ABC + {\text{Area of}}\,\Delta \,DCB\\ &= \frac{1}{2} \times (CB \times AO) + \frac{1}{2} \times (CB \times OD)\\&= \frac{}{2}CB \times (AO + OD)\\ &= \frac{1}{2} \times CB \times AD\\& = \frac{1}{2} \times 12\,{\rm{m}} \times 7.5\,{\rm{m}}\\ &= 45.0\,{{\rm{m}}^2}\end{align}\]

Thus, area of the rhombus is \(45.0\,{{\rm{m}}^2}\)