# How to Find the Perimeter and Area of a Trapezoid

## Area and Perimeter of a Trapezoid

Hi, and welcome to this video on finding the area and perimeter of a trapezoid!

A trapezoid is a four-sided polygon, or “quadrilateral”, that has at least one set of parallel sides. There are two types of sides in a trapezoid: legs and bases. A trapezoid has two legs and two bases.

We can tell which sides are the bases because they are parallel to each other. Here, we can see the top and bottom are parallel because of the matching arrows on those sides. When we know the lengths of the legs and the lengths of the bases we can find the **perimeter** of the trapezoid.

The perimeter is the distance around an object. For instance, if we wanted to build a fence around a trapezoid-shaped yard, we’d need to know the perimeter of the yard to know how much fencing to buy.

For a trapezoid, the formula for perimeter is “The perimeter of a trapezoid, P equals the measure of base one plus the measure of base two plus the measure of leg one plus the measure of leg two.”

We don’t need to remember this formula though, because just like with every other type of polygon it’s just a fancy way of saying **add all of the sides together**!

Let’s go ahead and find the perimeter of this trapezoid:

That’s all there is to it! Let’s move on to **area**. Here’s a trapezoid on some graph paper:

Remember that area is a measure of how many square units will fit inside a shape. How many squares are inside our trapezoid?

There are 24 full squares plus eight half squares, which means the area of the trapezoid is 28 square units. But what if we don’t have graph paper or a conveniently-sized trapezoid? That’s why we need a formula!

The formula for finding the **area** of a trapezoid is: “The area of a trapezoid, A, equals h, the height of the trapezoid, times the length of base one plus the length of base two divided by two.”

Note that dividing the sum of the bases by two is the average of those lengths. Because our sample problem is on a graph, we can see that the top base, which we’ll call base 1, is three units long. Our bottom base, base 2, is 11 units longs. The height of the trapezoid, which is the distance between the bases, is four units:

For area, we don’t need the measurements of the two legs, just the two bases and the height, which can also be called the **altitude**. Since we have all three we can plug them into our formula:

That’s the same answer we got when we counted!

Let’s try another one:

Okay, it looks a bit different than the trapezoid we just did. But we can tell it’s a trapezoid because it has one set of **parallel sides**. We can use the formula, so now we just need to figure out which numbers go where. The parallel sides are the bases so we can set base one as 6 centimeters and base two as 3 centimeters. There’s no dashed or colored line inside the trapezoid connecting the bases that would clearly be the height, but the bottom side is connecting the bases and is perpendicular to them, as we can tell by the right angle symbol. So 4 centimeters is the height, even though it’s sideways! Let’s plug it all in:

This formula also works to find the area of parallelograms too. That’s because all parallelograms are trapezoids since they have at least one set of parallel sides. In fact, all parallelograms have two sets.

That’s about all there is to finding the perimeter and area of trapezoids.

Thanks for watching, and happy studying!