For example, in trapezoid known length of parallel sides (a and b, respectively), and also the length of its height h, then calculate the area of a trapezoid by applying the following formula:
S = ((a+b)*h)/2
Example: the length of the base and the opposite side of the trapezoid is 28 and 22 cm, respectively. The height of this trapezoid is 30 cm
In order to find the area of this shape, it is necessary to use the formula given above:
S = ((28+22)*30)/2 = 750 cm2
When the trapeze is known the length of its middle line m and its height is h, find the area of a trapezoid becomes even easier, knowing this formula:
S = m*h
Example: length of the midline of the trapezoid is 15 cm, its height is 10 cm
Applying the above formula, is obtained:
S = 15*10 = 150 cm2
For example, given an isosceles trapezoid, around which described a circle whose radius is equal to r and the base angle of the trapezoid is equal to α. In this case, the area is calculated this way:
S = (4*r2)/sinα
Example: around an isosceles trapezoid circumscribed circle with a radius of 20 cm, the base angle of the trapezoid is equal to 45°. Then the area is as follows:
S = (4*152)/sin45°
S = 1273 cm2