# How to find the height of the trapezoid, if we know the area

Under trapeze means a quadrilateral in which two of its four sides are parallel to each other. The parallel sides are the bases of the trapezoid, the two others are the sides of the trapezoid. Find the height of the trapezoid, if you know the area it will be very easy.

## Instruction how to find the height of the trapezoid, if we know the area

Step 1:

It is necessary to understand how to calculate the area of the original trapezoid. For this purpose there are several formulas, depending on the initial data: S = ((a + b) * h) / 2, where a and b - length of the trapezium bases and h - its height (height of the trapezoid - the perpendicular dropped from one base trapeze to another); S = m * h, where m - the average shedding trapezoid (Average shedding - segment parallel bases of the trapezoid and the connecting middle of its sides).

Step 2:

Now, knowing the formula for calculating the area of a trapezoid, one can derive new location for the trapezoid height: h = (2 * S) / (a + b); h = S / m.

Step 3:

To make it clearer how to solve such problems, you can see examples: Example 1: Dana trapezoid, whose area is 68 cm², an average shedding which is 8 cm, is required to find the height of the trapezoid. To solve this problem, it is required to use the previously derived formula: h = 68/8 = 8.5 smOtvet: the height of the trapezoid is 8.5 smPrimer 2: Let the trapezoid area is 120 cm², of the bases of the trapezoid equal the length of 8 cm and 12 cm respectively , it is required to find the height of the trapezoid. To do this, use one of the derived formulas: h = (2 * 120) / (8 + 12) = 240/20 = 12 smOtvet height given trapezium is 12 cm