# How to Find the Area of a Trapezoid

We have learned how to calculate the areas of a **square, rectangle**, **parallelogram**, and **circle**. In this post, we are going to learn how to find the area of a trapezoid. This is the first post of **Finding the Area of a Trapezoid Series**.

A trapezoid is a polygon whose exactly one pair of sides are parallel*. The figure below is a trapezoid where sides *a* and *b* are parallel.

Notice that if we make another trapezoid which has the same size and shape as above, flip one trapezoid, and make one pair of the non-parallel sides meet, we can form the figure below. That figure is a parallelogram. Can you see why?

Now, observe that the *base* of the parallelogram from the figure is *a* + *b*. Its height is *h. *

We have learned that the **area of a parallelogram **is the product of its base and height. So, the expression that describes its area is

.

Now, when we calculated for the area of the parallelogram above, we actually calculated the area of two trapezoids. Therefore, to get the area of a trapezoid, the have divide the formula above by 2 or multiply it by . That is, if we let be the area of a trapezoid is

where *a* and* b* are the base (parallel sides) and *h* is the height.

*Please take note that there are other definitions of this polygon. In some books, it is defined as polygons whose at least one pair of sides are parallel.

**Example 1**

What is the area of a trapezoid whose base are 12 cm and 18 cm and whose height is 15 cm.

*Solution*

Using the notation above, in this problem we have , and ?

The formula for area is

So, substituting we have

So, the area of the trapezoid is 225 square units.

In the **next part** of this series, we will have more examples on calculating the area of a trapezoid.

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[…] How to Find the Area of a Trapezoid Part 1 discusses the derivation of the formula. The derivation uses the two trapezoids to form a parallelogram and since the formula for finding the area of a parallelogram has been discussed, it can be used for computation. In this post, an example was also shown on how to find the area of a trapezoid. […]

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