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

$h(a + b)$.

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 $\frac{1}{2}$. That is, if we let $A$ be the area of a trapezoid is

$A = \frac{1}{2}h( a + b)$

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 $a = 12$, $b = 18$ and $h = 15$?

The formula for area is

$A = \frac{1}{2}h(a + b)$

So, substituting we have

$A = \frac{1}{2} (15)(18 + 12) = 225$

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.