By Damon Verial, Updated Aug 30, 2022
Determining the height of a trapezoid can be tricky because it rarely aligns with one of the shape’s edges. By leveraging the area formula, you can derive the height with a straightforward algebraic rearrangement.
Begin with the standard trapezoid area equation: \[ A = \frac{h\,(b_1 + b_2)}{2}\] where A is the area, b_1 and b_2 are the lengths of the two parallel bases, and h is the height.
Multiply both sides by 2: \[ 2A = h\,(b_1 + b_2)\] Then divide by the sum of the bases: \[ h = \frac{2A}{b_1 + b_2}\] This expression gives the height directly in terms of the known area and base lengths.
For example, if a trapezoid has bases of 4 units and 12 units and an area of 128 square units, substitute into the formula: \[ h = \frac{2\times128}{4+12} = \frac{256}{16} = 16\] Thus, the height is 16 units.
Using this method, you can quickly determine the height for any trapezoid when the area and base lengths are known.
