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The Simple Formula for How to find Area of a Trapezoid

Get the free Area of a Trapezoid worksheet and other resources for teaching & understanding how to find Area of a Trapezoid

Here’s how to find Area of a Trapezoid

A trapezoid is a 2-D four sided figure that has one set of parallel sides. The other two sides are not parallel. The parallel sides of a trapezoid will be different lengths. In order to solve how to find the Area of a Trapezoid you must add the two parallel sides together, multiply that sum by the height, and then finally divide by two. The height of a trapezoid must be perpendicular to the base of the trapezoid. When finding the Area of a Trapezoid you cannot use the sides of the trapezoid because they are not perpendicular with the base of the trapezoid. Typically, you will see a dotted line in a trapezoid that represents the height.

Common Core Standard: 6.G.1

A Short Summary for Finding Area of a Trapezoid

So how do you find the area of a trapezoid anyway? A trapezoid is a 2-D four sided shape that has one pair of parallel sides. The other opposite sides are not parallel. The parallel sides of a trapezoid will be made up of lengths that are not equal. When answering how to find the Area of a Trapezoid you have to follow the Area of a Trapezoid formula. You first find the sum of the two parallel sides, then you multiply that total by the height of the trapezoid, and lastly divide by two. A trapezoids height will be 90 degrees with the base. When finding the Area of a Trapezoid you cannot utilize the sides of the trapezoid since they are not 90 degrees with the base of the trapezoid. Usually, you will see a dashed line in the trapezoid that illustrates the height.

4 Simple Steps for Solving Area of a Trapezoid Example Problems

1. Add the lengths of the two parallel sides together.
2. Multiply the sum of the two parallel sides times the height.
3. Divide the answer by two.
4. Make sure you use the correct unit measure.

Area of a Trapezoid Practice Problems Quiz

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Area of a Trapezoid Quiz

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Find the area of this trapezoid.

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Find the area of this trapezoid.

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Find the area of this trapezoid.

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Find the area of this trapezoid.

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Find the area of this trapezoid.

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Watch the Video Explanation of our Area of a Trapezoid Worksheet

Watch our free video on how to find Area of Trapezoid. This video shows how to solve problems that are on our free Area of Trapezoid worksheet that you can get by submitting your email above.

Watch the free Area of a Trapezoid video on YouTube here: Area of a Trapezoid Video

Video Transcript:

This video is about how to get the area of a trapezoid formula. You can get the trapezoid area worksheet used in this video for free by clicking on the link in the description below. A trapezoid is any four-sided figure that has one set of parallel sides. In order to find area of a trapezoid you’re going to take the length of the longer base, which we’re going to say is b sub 1 plus the length of the shorter base, which is b sub 2 divided by 2 and then multiplying that by the height. This is the general rule for area trapezoid formula.

In the case of this example here, that has a base length of 16, a second base length of 8, and then a height of 12 feet. The bases are the outer edges of the trapezoid. I know that 16 is going to be the longer base because it is the bigger base of the two. 16 is larger than eight so I know it’s the first base. Then we have the second base which is going to be eight feet because it is the shorter length of the two base lengths. And then I know that 12 feet is going to represent the height because it is the distance between the two parallel sides. We know the formula for area of a trapezoid is the long base plus the short base divided by two and then multiplying times the height. In the case of our example we know the long side is 16. We’re going to say 16 plus the short side, which in this case is eight, and then we’re dividing by two and then multiplying by the height which is 12 in this example. When we simplify for our area of a trapezoid, we’re going to do 16 plus 8 which is 24 divided by 2 and then multiplying by 12. Now our area is 24 divided by 2 so that’s 12 and then times 12. We multiply 12 times 12 and that’s going to give us 144. And then our units are feet so it’s 144 feet squared. Our answer to this area of a trapezoid is 144 feet squared. The big thing to remember is that the height is the distance between the two parallel sides and then the bases are the side lengths that are on the outside of the trapezoid area formula.

Let’s do a couple practice problems on our area of a trapezoid worksheet. The first problem on how area of a trapezoid worksheet gives us side lengths of 15 and 4 and a height of 8 inches. In order to show you how to find the area of this trapezoid we’re going to use our formula area equals the long base plus the short base divided by two and then multiplying by the height. In the case of number one I know that the long side is 15 inches and I know that the short side is 4 inches. The height has to be 8 inches because this dotted line represents the distance between the two parallel sides. We take our information and we substitute each piece into our area of a trapezoid formula. The first part is the side length of the long side, which is 15 inches, plus the side length of the short side, which is four inches, and we’re dividing that by 2. And then we multiply all of that with the height, which is 8 inches. Now we’re going to simplify our formula 15 plus 4 is 19 divided by 2 and then times the height which is 8. Then we’re going to simplify 19 divided by 2 and that’s 9.5 and then we’re going to multiply times the height which is 8 to get a solution of 76 inches squared as our final answer.

The second problem showing how to find the area of a trapezoid 6th grade on our area of a trapezoid worksheet that we’re going to use to show you finding the area of a trapezoid is number two. We know our formula is area equals the long side base plus the short side base divided by two and then multiplying times the height. In the case of problem 2 on our area of a trapezoid worksheet we know that the long side is 20 because it’s the outer edge of the trapezoid and it gives us 20. We know the short side is going to be four inches and then we know that the height, which is the distance between the two parallel sides, is going to be 14 inches. Now we’re going to substitute all of them into our formula. The long side is 20 so we’re going to say 20 inches, plus the short side which is 4 inches, so we’re going to say 4 inches, divided by 2 and then multiply times the height, which in this case is 14 inches. Then we’re going to simplify 20 plus 4, that’s 24. We still have to divide by 2 and we still have to multiply times the height which is 14. That final step would be to take the 24 divided by 2 to get 12 and we’re still going to multiply that times the height which is 14 to get a final solution of 168 and our units are inches. The final solution is 168 inches squared.

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