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Math & Statisticsgeometry

Trapezoid Calculator

Trapezoid area from the two parallel sides and the height. The area is the median times the height, which is the same rule as a rectangle with the average width.

Also called: trapezium calculator.

Area
32

Area 32, from the average of the two parallel sides (8) times the height (4). The perimeter is 26.

Median, the average of the parallel sides
8
Perimeter
26
Height
4
Type of trapezoid
Isosceles, since the slant sides are equal.
How this is calculated
Method and background

How this is calculated

Averaging the two parallel sides gives the median, and multiplying by the perpendicular height gives the area. That works because a trapezoid can be rearranged into a rectangle of the median width. The height must be the perpendicular distance between the parallel sides, not the length of a slant side, which is the usual mistake.

area = the average of the two parallel sides, times the height between them
a, b
The parallel sides
h
Perpendicular height

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

a standard trapezoid

First parallel side
10
Second parallel side
6
Height between them
4
First slant side
5
Second slant side
5

Area32

arithmetic identity

Open this example

equal parallel sides make a parallelogram

First parallel side
8
Second parallel side
8
Height between them
4
First slant side
5
Second slant side
5

Area32

boundary

Open this example

Method and limits

What it assumes

  • The height entered is perpendicular to both parallel sides.

What it deliberately does not model

  • The perimeter needs both slant sides; without them only the area is returned.

Formula version 1.0.0 · definition 1.0.0 · India · Report a problem with this calculator

Frequently asked questions

Is the height a slant side?
No. It is the perpendicular distance between the two parallel sides. Using a slant length overstates the area.