# Measuring the Area of a Rhombus: Formula & Examples

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• 0:07 A Rhombus
• 1:53 Altitude & Side
• 2:31 Side & Angle
• 4:05 Diagonals
• 5:15 Lesson Summary

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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Did you know that there are three ways to find the area of a rhombus? Watch this video lesson to learn all three of them. See what information you need for each method as well as the steps required for each.

## A Rhombus

First, let's go over what a rhombus is. A rhombus is a four-sided shape whose sides are all equal and whose opposite sides are parallel. If you are given the measurement of just one side, then you also know the measurement of all the other sides since they are all equal.

A rhombus has five additional measurements that we can consider. I've marked them down on the rhombus below so you can see them. If you look at the red dashed line going straight up and down, that is the altitude, or the height of the rhombus. It is not how long the side is but how high the rhombus is if it was sitting on a flat surface. Note how the bottom side is flat. The next two measurements are the diagonals, the lines connecting the opposite angles to each other. I've drawn the diagonals using blue dashed lines. Do you see them? I've labeled one diagonal p and the other q so you know which is which.

The red s is the measurement for the length of a side. If one side is marked s, then all the other sides are also s because all the sides of a rhombus are equal in length to each other. The fourth and fifth measurements we can note are the measurements of the angles. We can call one pair of opposite angles Angle A and the other opposite pair of angles Angle B. It doesn't matter how you label these as long as you label one pair one name and the other pair another name.

Now that we have all of our various measurements that we can consider, let's go over the three different ways to find the area of a rhombus. I encourage you to commit these three formulas to memory. Use flashcards or whatever memory aid that helps you.

## Using the Altitude and Side

One way to find the area of a rhombus is by using the altitude and the side. If we know these two measurements, then we can use this method. The formula for this method is:

Area = Altitude * s

Looks pretty simple, right? All you have to do is to multiply the altitude with one of the sides. It doesn't matter which side, as they're all the same.

So, if you had a rhombus whose altitude is 6 inches with sides that are 2 inches, then the area of this rhombus is 6 inches * 2 inches = 12 inches squared.

## Using the Side and Angle

Now, if instead of the altitude, you are given one of the angle measurements, you can use another method for finding the area of a rhombus. This method uses the side measurement and one of the angle measurements, and the formula looks like this:

Area = s^2 sin (A) or Area = s^2 sin (B)

The formula is the same regardless of which angle you are given. All you need is the measurement of one of the angles and the side. You also multiply here, but first you have to find the sine of the angle as well as squaring your side. This formula is a bit harder to memorize than the one using the altitude and side, but it is still a good idea to commit this to memory. Write it down on a flashcard if you need to.

If our rhombus tells us that our side measures 2 inches and one of our angles measures 60 degrees, then to find the area of this rhombus, we would plug this into our formula for area using the side and an angle.

Area = 2^2 sin (60)

We square our side, and find the sine of 60 degrees. So:

Area = 4 * 0.866

Then, we multiply these two numbers together to get our answer.

Area = 3.46 inches squared

I want you to remember that for this method the angle you choose does not matter. The formula is the same for both angles; you just have to pick one of them to use.

## Using the Diagonals

The last way of finding the area of a rhombus uses only the two diagonals. The formula looks like this:

Area = (p * q)/2

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