How to find the trapeze height if the area is known

The trapeze is meant as a quadrangle at which two of four of its parties are parallel among themselves. The parallel parties are the bases of this trapeze, two others are lateral faces of this trapeze. To find the trapeze height if its area is known, it will be very easy.

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1

It is necessary to understand as it is possible to calculate the area of an initial trapeze. For this purpose there are some formulas, depending on basic data:

S = (*h (a+b))/2, where an and b - lengths of the bases of a trapeze, and h - its height (Trapeze height - the perpendicular lowered from one basis of a trapeze to another);

S = m*h where m - average fading trapezes (Average fading - the piece parallel the bases of a trapeze and connecting the middle of its lateral faces).

2

Now, knowing formulas for calculation of the area of a trapeze, it is possible to bring out of them new, for finding of height of a trapeze:

h = (2*S)/(a+b);

h = S/m.

3

In order that it was more clear how to solve similar problems, it is possible to review examples:

Example 1: The trapeze at which the area is equal 68 cm is given?, average fading which it is equal 8 cm, it is required to find height of this trapeze. To solve this problem, it is required to use earlier removed formula:

h = 68/8 = 8.5 cm

Answer: height of this trapeze makes 8.5 cm

Example 2: Let at a trapeze the area equal 120 cm?, lengths of the bases of this trapeze are equal 8 cm and 12 cm respectively, it is required to find height of this trapeze. For this purpose it is necessary to apply one of the removed formulas:

h = (2*120) / (8+12) = 240/20 = 12 cm

Answer: height of the set trapeze is equal 12 cm