# Area Of A Trapezoid

When you talk of a trapezoid, it is a quadrilateral that has two parallel sides having different lengths. In a trapezoid, the parallels sides having different lengths can be the base. One unique aspect about a trapezoid is that is has two bases. In this post, we show you how you can find the area of a trapezoid.

This is how a trapezoid looks like. The first step involves identifying the length of the two bases. These are the two sides that run parallel to each other. You can call these sides a and b.

So, let’s say that side a is 10 cm long and side b is 12 cm long. The next step with be adding the lengths of the two bases.

So, it will 10 cm + 12 cm =22 cm

The formula for calculating the area of a trapezoid is {(b1 + b2) x h} /2

In other words, you find the area of a trapezoid by adding the two bases and multiplying by the height and then dividing by two. Now, in the above formula, b1 stands for base one, and b2 represents base two while h represents the height.

This means that you also need to identify the height of the trapezoid. Usually, the height is the line that runs perpendicular to the two bases.  Let’s say that in our example, the height is 6 cm.

You will therefore need to take the formula and plug in the values.

Area = {(b1 + b2) x h} /2

Area = {(10 + 12) x 6} /2

Area = {22 x 6} /2

Area = 66

The reason why you have to divide by two is because you want to find the average of the two bases. You will add the lengths of the bases and divide them by two before you multiply by the height.

You can also find b1 or b2 values if you are given the area and one of the bases and the height.

For example, if you are given one of the bases as 15 cm and the other is unknown, and you are also given the height as 10 cm and the area as 100 cm2, you can find the unknown base. This is how to go about it:

You write down the formula:

Area = {(b1 + b2) x h} /2

Let’s imagine that base value we are given as 15 cm is for b1, so we want to find b2. In this case,

100 = {(15 + b2) x 10} /2

100 = {(15 x 10) + (10b2)} / 2

100 = (150 + 10b2) / 2

100 = 75 + 5b2

100 – 75 = 5b2

25 = 5b2

Therefore, b2 = 25 divided by 5