# How to Find the Perimeter and Area of a Trapezoid

## Area and Perimeter of a Trapezoid

Recall that a trapezoid as a quadrilateral, or four-sided figure, with exactly 1 pair of opposite sides parallel. To find the area of a trapezoid, we’re going to take half of the product of the height, and the quantity base 1 plus base 2.

The bases are those parallel sides, that 1 pair of opposite sides that’s parallel– those are your bases. The height is the perpendicular distance between the bases; the height must be perpendicular to the bases. To find perimeter, again we’re just going to add all the sides, perimeter is just the distance around.

**Perimeter** is side 1 plus side 2, plus base 1, plus base 2 just add all four of the sides together. Let’s look at this example. Find the area and perimeter of the trapezoid below. First we’ll find the area, and we’re going to start by writing our formula.

The **area** of a trapezoid is 1/2 the product of the height, times the quantity base 1, plus base 2. Then we need to substitute our values. Area is 1/2 times the height, (and the height, again, is the perpendicular distance between the bases) so our height is 9 meters, times the quantity base 1, plus base 2, (again, the bases are those parallel sides) so 13 meters and 17 meters, because that’s the pair of parallel sides, so those are our bases (13 meters plus 17 meters).

It doesn’t matter the order you add those because 13 meters plus 17 meters is the same as 17 meters plus 13 meters. Again, we need to follow PEMDAS, or our order of operations, so I’m going to start with our parentheses here, 13 meters plus 17 meters. 1/2 times 9 meters, times 10 and 10 is 20, 3 and 7 is another 10, 20 and 10 gives me 30 meters.

Now it’s up to you which number to take half of, you can do this in any order you want. You can multiply half times 9 first, and then take that product times 30, or you can take half of 30, and multiply that times 9 meters, or you can multiply 9 meters times 30 meters, and then take half of that.

It’s up to you, whichever you think is the easiest. I think what I’m going to do is take half of 30 meters, so half of 30 meters is 15 meters. 15 meters times 9 meters, 10 times 9 is 90, and 5 times 9 is 45, so 90 plus 45 gives us 135, and then meters times meters is meters squared.

Our area is 135 meters squared. Now to find our perimeter. The perimeter, again, is just when we add up all the sides. Side 1 plus side 2, plus base 1, plus base 2. Now we need to substitute our sides, (and it doesn’t matter which 1 of these you call side 1 or side 2) 12 meters plus 11 meters, plus base 1, 13 meters (and also it doesn’t matter which base you consider to be base 1 or base 2, those are also interchangeable) plus base 2, 17 meters.

Then since we’re adding, again we can add in any order we want, so we could start back here with 13 meters plus 17 meters (we did that just a minute ago, and we got 30 meters). 13 meters plus 17 meters is 30 meters, plus 11 meters, 41 plus 12, 53. The perimeter is 53 meters.