How to find the area of a trapezoid?

The area of ​​the trapezoid will be equal to the half-sum of its bases multiplied by the height. In the form of a formula, this is written in the form of the expression S = ((a + b) * h) / 2, where S is the area of ​​the trapezoid, a, b is the length of each of the bases of the trapezoid, h is the height of the trapezoid.

There is another simple formula for calculating its area. According to it, the area of ​​the trapezoid is equal to the product of its midline by the height of the trapezoid and is written as: S = m * h, where S is the area, m is the length of the midline, h is the height of the trapezoid. This formula is more suitable for problems in mathematics than for everyday problems, since in real conditions you will not know the length of the center line without preliminary calculations. And you will only know the lengths of the bases and sides.
In this case, the area of ​​the trapezoid can be found by the formula:

S = ((a + b) / 2) * √ c ^ 2 – ((b – a) ^ 2 + c ^ 2 – d ^ 2/2 (b – a)) ^ 2

where S is the area, a, b are the bases, c, d are the sides of the trapezoid.