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Geometry: High School15 chapters | 160 lessons

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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.

Watch this video lesson to learn the simple formula to find the area of a parallelogram. Learn what measurements you need, how to label your parallelogram, and how to use the formula.

A **parallelogram** is a four-sided flat shape with two pairs of equal parallel sides. This is to say that the opposite sides of a parallelogram are both equal to each other and parallel. The two pairs of opposite sides do not necessarily have to be the same length. You can have two different lengths for the two pairs.

A good way to picture a parallelogram is to picture a leaning box. If you take a moving box and punch out the ends, lean it against a wall, and then look at the opening, you would be looking at a parallelogram. It's a leaning rectangle!

In order to find the area of a parallelogram, we need to label our measurements. There are only two measurements that we need to be concerned about. If our parallelogram is sitting on a flat surface, the first measurement we need is the length of the bottom side. This we can label with a *b* for base. We call this the base because it is the bottom of the parallelogram.

The next measurement we need is the height of the parallelogram. This is the straight up and down measurement from the bottom to the top. We can label this measurement *h* for height. Note that this is not how long the leaning sides are, but the distance between the bottom side and the top side.

The formula to find the area of a parallelogram is this one:

Area = *b* * *h*.

Do your best to memorize this formula for the area of a parallelogram. With your parallelogram sitting flat, remember that to find the area, all you need is to multiply the length of the flat sides with how tall the parallelogram is. Only two numbers to worry about.

Let's see how this formula works with an example.

We have a parallelogram here:

I see that it's sitting flat. I also see that the flat sides measure 6 inches, the leaning sides measure 4 inches, and it has a height of 3 inches.

I remember that the only two measurements I need to worry about are the length of the flat sides and the height. This problem gives me more information than I need. So, what do I do with the extra information? I am going to just leave it be. I don't need to use it, so I can essentially ignore it. I am only going to focus on the numbers that I need, which are the base at 6 inches and the height at 3 inches.

Now, I can take my formula and plug in my values.

Area = *b* * *h*

Area = 6 inches * 3 inches

Area = 18 inches squared

The calculation is straightforward after I plug in my values. The formula tells me to multiply the two numbers, which I have done. So, my answer is 18 inches squared. I also remember that for area, my answer should always end with my measuring units squared. My answer does end with my measuring units squared, so I am done.

What have we learned? We have learned that a **parallelogram** is a four-sided flat shape with two pairs of equal parallel sides. It looks like a leaning rectangle. The formula to find the area of a parallelogram is:

Area = *b* * *h*.

With the parallelogram sitting flat, the *b* stands for the base, or the side that is flat on the ground, and the *h* stands for height, or the distance between the bottom and top sides. Once we have these two measurements, we can disregard any extra information that we may be given. The formula tells us to simply multiply the base with the height to get our answer. And remember, the area always ends with your measuring units squared.

After completing this lesson, you should be able to:

- Define parallelogram
- Identify the formula and measurements needed to find the area of a parallelogram

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Geometry: High School15 chapters | 160 lessons

- Parallelograms: Definition, Properties, and Proof Theorems 5:20
- Measuring the Area of a Parallelogram: Formula & Examples 4:02
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