A common task in geometry is calculate the area of a trapezoid. This requires memorizing a formula, and the ability to correctly identify the dimensions of the trapezoid. You also have to be completely sure about what a trapeze is and is not. This OneHowTo article shows the steps to do so, and offers a suggestion on how to understand and memorize the formula for calculating the area of a trapezoid.
In non-mathematical terms, a trapezoid starts out as a rectangle, but the left and right sides are slanted inward. The top and bottom sides (known as the bases) are parallel, and are usually of different lengths. In an isosceles trapezoid, the left and right sides slope at the same angle, so they are congruent (same length). This is not the case for all trapezoids, as can be seen in the following image of an irregular trapezoid.
Most students know that the area of a rectangle is length times width. It is logical that a trapezoid – it is a variant of a rectangle – has a similar formula. It is so, with some modifications. To find the area of a trapezoid, you must multiply the height times the average of the two bases.
Bases are defined (in simpler terms), as the distances along the top and bottom. Height is measured from the top down. DO NOT measure the height along one of the slanted sides, because it is longer than the distance in a straight line. If they give you the measurement of one of the sloping sides, they probably want to fool you. You must still get, by any means, the measurement of the distance from the top to the bottom (the true height).
You may see the formula written in a different way than shown here, but all versions are equivalent. In this version, you are taking the mean of the two bases by adding them, and dividing the sum by 2. Next, the result is multiplied by the height.
That’s all there is to it, at least when it comes to the fundamentals. Sometimes a problem requires you to do some calculations to determine the lengths of the bases or the height if they are not provided. This sometimes requires the use of the Pythagorean Theorem or other geometric methods, which are beyond the scope of this article. Make sure you memorize the formula, practice it, and that you can distinguish trapezoids from other geometric shapes.
