What Is the Trapezoid Height Calculator?
A trapezoid (or trapezium) is a four-sided shape with one pair of parallel sides, called the bases. Its area depends on those two bases and the perpendicular distance between them — the height. This calculator works the area formula backwards: if you already know the area and both parallel sides, it solves for the height instantly.
How to Use It
Enter the area (A) of the trapezoid, then the lengths of the two parallel sides, base a and base b. Press calculate and the tool returns the height in the same units (consistent throughout — for example, area in cm² with bases in cm gives height in cm).
The Formula Explained
The area of a trapezoid is \(A = \tfrac{1}{2}(a + b) \times h\). Rearranging to isolate \(h\) gives:
$$h = \frac{2A}{a + b}$$
In words: multiply the area by two, then divide by the sum of the two parallel bases. The non-parallel (slanted) sides are not needed for this calculation.
Worked Example
Suppose a trapezoid has an area of 50 square units, with parallel bases of 8 and 12 units. Then \(a + b = 20\), and $$h = \frac{2 \times 50}{20} = \frac{100}{20} = 5 \text{ units}$$ You can verify: $$A = \tfrac{1}{2}(8 + 12) \times 5 = \tfrac{1}{2} \times 20 \times 5 = 50 \checkmark$$
FAQ
Does it matter which base is a and which is b? No — addition is commutative, so \(a + b\) gives the same result either way.
What units does the height use? The same linear unit as your bases, provided your area uses the squared version of that unit.
Can I use it for an isosceles trapezoid? Yes. The height formula only depends on area and the two parallel bases, regardless of whether the legs are equal.
