Trapezoid Calculator

Written byOleh Soloninupdated 27 September 2026

What you know

Base a

Base b

Height

Side c

Used for the perimeter; required when you know all four sides.

Side d

Result

Area28
WorkingS = (10 + 4) ÷ 2 · 4 = 28
Midline7
Height4
Perimeter24
Leg projection (isosceles trapezoid)3

Average the parallel sides, multiply by height

Area from the two parallel sides and the height, plus the midline, perimeter and, for an isosceles trapezoid, the horizontal projection of each leg.

The area of a trapezoid is the average of the two parallel sides times the height. That average is also the midline, so the formula reads as "midline times height", which is far easier to remember.

The height is the perpendicular between the parallel sides, not the slanted side. Confusing them is the standard mistake: on any non-right trapezoid the slanted side is always longer than the height.

How to use

Choose what you know: the two parallel sides with the height, or the sides themselves.
Enter the measurements.
Read the area, the midline, the perimeter and the working.

Area through the midline

The midline equals half the sum of the parallel sides, and the area is that midline times the height. With bases of 10 and 4 the midline is 7, so a height of 4 gives an area of 28.

It follows that every trapezoid has the same area as a rectangle of the same height whose width is the midline. The height is always the perpendicular between the parallel sides, never the length of a slanted one.

In the last row the bases are equal, which makes it a parallelogram; the formula still gives its area, base × height. Worked out with this calculator.
Bases	Height	Midline	Area
10 and 4	4	7	28
10 and 4	8	7	56
12 and 6	5	9	45
7 and 7	4	7	28

What this calculator shows

The area and the length of the midline
The perimeter, once both slanted sides are entered
For an isosceles trapezoid, the horizontal projection of each leg — half the difference between the bases

What to keep in mind

The height must be perpendicular to the parallel sides; a slanted side will not do.
The formula is identical for right and isosceles trapezoids — the shape does not change the area rule.

FAQs

What is the midline?

The segment joining the midpoints of the slanted sides. It runs parallel to the bases and equals half their sum. Multiplying it by the height gives the area, which makes a trapezoid equal to a rectangle of the same height.

How do I find the height from the area?

Divide twice the area by the sum of the bases. That check is printed as its own line so the result can be verified.

What makes a trapezoid isosceles?

Equal slanted sides, equal base angles and equal diagonals. It does not change the area formula but makes finding the height from a side straightforward.

Can I get the area without the height?

There is a Heron-like formula using all four sides, but it is unwieldy; finding the height from the triangle formed by the legs and the difference of the bases is quicker. Either way the bases must differ: with equal bases the four sides no longer fix the height.

How is the area of a trapezoid found?

Take half the sum of the parallel sides and multiply by the height. With bases of 10 and 4 and a height of 4 the area is 28, and the midline is 7.

Worked example

Bases of 10 and 6

Input: Bases 10 and 6, height 4

Output: Area 32, midline 8

Note: The midline is 8, exactly the average of the bases. A rectangle 8 by 4 has the same area, which is a quick way to sanity-check the answer.

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Trapezoid Calculator

Result

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