We can derive the formula of height from the Area formula of a trapezoid.
Area of a Trapezoid = ((a+b)/2) h
Where a is the length of the upper base, b is the length of the lower base, and h is the height of the trapezoid.
To get the height of the trapezoid : we must divide the Area by (a+b)/2 to find h..
For example: a = 10cm; b = 15cm; h = 8cm ; A =?
A = ((a + b) / 2) * h
A = ((10 + 15) / 2) * 8
A = (25/2) * 8
A = 12.5 * 8
A = 100 sq.cm
If A = 100, a = 10 , b = 15, h = ?
h = A / (a+b)/2
h = 100 / (10+15)/2 *in dividing fractions, find the reciprocal of the 2nd fraction
h = 100 / 25/2
h = 100 * 2/25 *multiply the first fraction to the reciprocal of the 2nd fraction
h = (100 * 2) / 25
h = 200 / 25 * simplify the fraction
h = 8