Trapezoid Calculator: Area, Midsegment, Bases

Three ways to solve a trapezoid

A trapezoid has exactly one pair of parallel sides, called the bases ($a$ and $b$). Depending on what you already know, this calculator solves it three ways:

1. Both bases and height — when you know $a$, $b$, and the perpendicular height $h$:

$m = \frac{a+b}{2} \qquad K = m \times h$

2. Area, one base, and height — solve for the other base:

$a = \frac{2A}{h} - b$

3. Area and both bases — solve for the height:

$h = \frac{2A}{a+b}$

Where the area formula comes from

Picture sliding a triangular sliver off one end of the trapezoid and attaching it to the other end: the result is a rectangle with the same height $h$ and a width equal to the average of the two bases. That average is exactly the midsegment $m = (a+b)/2$, so the trapezoid's area is $K = m \times h$ — identical in form to a rectangle's $A = \text{width} \times \text{height}$, just with the width replaced by an average.

Worked example: bases a = 6, b = 10, height h = 4

$m = \frac{6+10}{2} = 8 \qquad K = 8 \times 4 = 32$

✅ Area = 32, midsegment = 8.

Worked example: area A = 32, base b = 10, height h = 4 — find the other base

$a = \frac{2(32)}{4} - 10 = 16 - 10 = 6$

✅ The other base is 6 — matching the first example, since it's the same trapezoid viewed from a different known measure.

Worked example: area A = 32, bases a = 6, b = 10 — find the height

$h = \frac{2(32)}{6+10} = \frac{64}{16} = 4$

✅ Height = 4 — again the same trapezoid, solved from its third possible combination of knowns.

Common mistakes

• Using a leg instead of the height. The height is the perpendicular distance between the two bases, not the length of a slanted side.
• Forgetting to average the bases. Writing $K = (a+b) \times h$ instead of $K = \frac{a+b}{2} \times h$ doubles the true area.
• Confusing the midsegment with the height. The midsegment is a length parallel to the bases; the height is perpendicular to them — they measure different directions entirely.

Where this shows up

• Land surveying: an irregularly shaped plot with two roughly parallel edges is often approximated as a trapezoid to estimate its area.
• Civil engineering: canal and levee cross-sections are frequently trapezoidal, with the bases being the surface width and channel-bottom width.
• Numerical integration: the trapezoidal rule approximates the area under a curve by summing many thin trapezoids, each using this same $\frac{a+b}{2} \times h$ formula.

A trapezoid generalizes the parallelogram, rectangle, and square, all of which are trapezoids with a second pair of parallel sides added — every one of them still satisfies $K = m \times h$, just with $m$ simplifying to a single base length when $a = b$.