## Area of a Rhombus Lesson

### Rhombus Area Formula

A rhombus is a parallelogram with four equal sides, a pair of opposing equal acute angles, and a pair of opposing equal obtuse angles. The formula for area of a rhombus is given as:

**A = ^{pq}⁄_{2}**

Where *A* is the area, *p* is the short diagonal, and *q* is the long diagonal.

INTRODUCING

### Area of a Rhombus Example Problems

Let's go through a couple of example problems together to practice finding the area of a rhombus.

#### Example Problem 1

Find the area of a rhombus with diagonal lengths of 5 and 10.

Solution:

- Plugging the given dimensions into the area formula, we get:

A =^{pq}⁄_{2}

A =^{(5)(10)}⁄_{2}=^{50}⁄_{2}= 25 **The area is 25.**

#### Example Problem 2

A rhombus is measured to have an area of 72 square meters and a short diagonal of 6 meters. How long is the long diagonal in meters?

Solution:

- Let's plug the given dimensions into the area formula and then solve for the long diagonal
*q*.

A =^{pq}⁄_{2}

72 = (6)q

q = 12 **The long diagonal is 12 meters long.**