Enable contrast version

TutorMe Blog

2 Formula for Finding the Area of a Rhombus

Trying to find the area of a rhombus can be simple. Here, we’ll look at the two formulas for the area that don’t use trigonometry so you can find your answer without too many headaches.

You can use one of these two formulas to find the area of a rhombus:

area of a rhombus formula 1

In this formula, h is the length of the height and s is the length of any side.

area of a rhombus formula 2

Here, p and q are the lengths of your two diagonals.

Before we show you how to use these formulas, let's explain what a rhombus is.

What Is a Rhombus?

First and foremost, a rhombus is a parallelogram. It's a four-sided figure where the opposite sides are parallel and all sides have equal lengths. Both squares and rhombuses are considered parallelograms.

While squares have four equal sides and four right angles, a rhombus has four equal sides but may not have four sets of right angles. Instead, the sides of a rhombus contain one set of parallel sides with equal acute angles (less than 90°) and another set of parallel sides with equal obtuse angles (greater than 90°).

area of a rhombus: sample of a rhombus

Image credit: Desmos

Look at the angles in the rhombus above. As you can see, only the opposite angles of the rhombus match. We have one set of obtuse angles and one set of acute angles.

Finding the Area of a Rhombus: Method 1

In order to determine the area of the rhombus, you can use one of the following rhombus formula:

Finding the Area of a Rhombus: Method 1

Where h is the length of the height and s is the length of a side. We’ll apply the height and side lengths of the below rhombus:

height and side of a rhombus

Image credit: Desmos

area of a rhombus in square units

Remember, when calculating area, your answer should always be in square units.

Finding the Area of a Rhombus: Method 2

Finding the Area of a Rhombus: Method 2

In this second formula, p and q are the diagonals of the rhombus. Let's use the area formula to determine the area of the rhombus below:

diagonals of a rhombus

Image credit: Desmos

As you can see, the diagonals of a rhombus go from the vertex of an interior angle to its matching one. The lengths of the diagonals vary.

Let's use the given lengths and insert them into the area of a rhombus formula:

area of a rhombus formula

Now that we know the product of the diagonals, we divide by two to find the final area:

final area

It's Easy to Find the Area of a Rhombus

Finding the area of a rhombus is easy. You just need to remember the perimeter of a rhombus is made of four equal sides containing two separate sets of matching interior angles. These can (but do not have to) match.

You can then use the lengths of both the diagonals of a rhombus or the height and side length to determine the final area of a rhombus.

More Math Homework Help

BEST IN CLASS SINCE 2015
TutorMe homepage
Made in California by Zovio
© 2013 - 2021 TutorMe, LLC
High Contrast Mode
On
Off