How to calculate the area of ​​a trapeze

A common task in geometry is to calculate the area of ​​a trapezoid . This requires the memorization of a formula, and the ability to correctly identify the dimensions of the trapeze. You also have to be completely sure about what is and is not a trapeze. This article shows the steps for this, and offers a suggestion of how to understand and memorize the formula to calculate the area of ​​a trapezoid .

The two bases and the height of a trapeze

In nonmathematical terms, a trapezoid begins as a rectangle, but the left and right sides are tilted inward. The upper and lower sides (known as the bases) are parallel, and are usually of different lengths. In an isosceles trapezoid, the left and right sides are inclined at the same angle, so they are congruent (same length). This is not the case with all the trapezoids, as can be seen in the following image of an irregular trapezoid.

Formula of the area of ​​a trapeze

Most students know that the area of ​​a rectangle is long by wide. It is logical that a trapezoid - it is a variant of a rectangle - has a similar formula. It is like that, with some modifications. To calculate the area of ​​a trapezoid, you must multiply the height by the average of the two bases.

The bases are defined (in simpler terms), as the distances along the top and bottom. The height is measured from the top down. DO NOT measure the height along one of the inclined sides, because it is longer than the distance in a straight line. If they give you the measurement of one of the inclined sides, they are likely to cheat you. You must still obtain, by any means, the measurement of the distance from the top down (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 average of the two bases by adding them, and dividing the sum by 2. Next, multiply the result by the height.

That is all that needs to be done, at least as far as the fundamentals are concerned. 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.