How to find the area of a trapezoid

How to find the area of ​​a trapezoid?

A trapezoid is a quadrangle with twoparallel and two nonparallel sides to each other. There are several types of this geometric figure. So, if the trapezoid has the same length of sides, it is called isosceles. A rectangular trapezoid is a geometric figure whose one side is perpendicular to the base.

Anyway, no matter how this figure is, in theIn any case, you can determine its area. Teachers tell how to find the area of ​​the trapezoid in geometry lessons. Those who do not remember school lessons are addressed to this article.

How to find the area of ​​a trapezoid: the formula and the course of the solution

So, in order to determine the area of ​​this figure ABCD, it is necessary first of all to measure all its sides with a ruler. Next, write the results in the format "AB = ...", "BC = ...", "CD = ...", "DA = ...".

On the AB side, the middle-point K is marked. On the segment DA the point L is marked. It is also in the middle of the AD side. After this, it is necessary to connect points K and L. The resulting segment will become the middle line of the trapezoid ABCD. We measure it with the help of the same ruler. Further, it is necessary to drop the perpendicular from point C to the base of figure AD. We measure the resulting segment CE, which will become the height of the trapezium. KL (middle line) is called the letter m, and CE (height) is h. In this case, the area of ​​the figure is measured by the formulaS = m * h.

There are other options for calculating the area of ​​the trapezoid. So, the bottom base of the figure AD is called the letter b, the upper BC - a. In this case, the area is determined by the formula:S = 1/2 * (a + b) * h. In addition, to count, you can decompose the trapeze into simpler shapes (rectangle and triangles), count their areas and add the resulting data.

Rectangular and isosceles trapezium

Sometimes there may be a question about how to findthe area of ​​the rectangular trapezoid. It is worth noting that all the above methods are relevant for figures of this type. The same can be said of an isosceles trapezoid. Speaking about how to find the area of ​​an isosceles trapezoid, we can note the following. The angles of this figure for any of the bases will be equal. Due to the fact that the sides of this trapezium are also equal, the height can be calculated from the formulah = c * sin (x). Thus, you can finalize the final formula to:S = (a + b) * c * sin (x) * 1/2.

We also pay attention to the particular case of an isosceles trapezoid when the diagonals of the figure are perpendicular. In this case, we can use formulaS = (a + b) ^ 2/4.

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