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.

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:

1. Plugging the given dimensions into the area formula, we get:
   A = ^pq⁄₂
   A = ^(5)(10)⁄₂ = ⁵⁰⁄₂ = 25
2. 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:

1. 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
2. The long diagonal is 12 meters long.