How to Calculate the Area of Trapezoids

By Sara Ipatenco
Fundamental geometric shapes each have unique formulas for finding the enclosed area.

Area refers to how much space is inside of a shape, and it's a useful measurement for real-life tasks such as purchasing the correct amount of flooring or planning how much grass to put down in an area of your backyard. A trapezoid is a four-sided shape with two parallel sides, one of which is longer than the other. The formula for finding the area of a trapezoid is 1/2(a+b)h, or the length of the top added to the length of the bottom, divided in half and then multiplied by the height of the trapezoid. The final number is represented as a squared number.

Measure the shorter of the two parallel sides, which will be represented by the letter "a" in the area formula for a trapezoid. For this example, "a" will be 9 inches long. Write this number down.

Measure the longer of the two parallel sides, which will be represented by the letter "b" in the area formula. For this example, the "b" will be 14 inches long. Write this number down as well.

Add the lengths of "a" and "b" together. For this example, your answer will be 23 inches. Record this sum.

Divide this sum in half, which will give you 11.5 inches as your answer. Record this number.

Identify the height of the trapezoid. Get this measurement by placing the zero mark of your ruler at "a" and adjusting your ruler to be at a 90-degree angle, or perpendicular, to "a." Measure the distance to "b" to get the height of the trapezoid. For the purpose of this example, the height is 8 inches.

Multiply the sum of the top and bottom of the trapezoid, divided by two, by the height of the trapezoid. For this example, you would multiply 11.5 inches by 8 inches to reach a product of 92 inches.

Represent your answer in squared form, which means the area of this trapezoid would be represented as 92 inches squared, or 92 square inches.

About the Author

Sara Ipatenco has taught writing, health and nutrition. She started writing in 2007 and has been published in Teaching Tolerance magazine. Ipatenco holds a bachelor's degree and a master's degree in education, both from the University of Denver.