Area of a trapezoid
Calculator and formulas for calculating the area of a trapezoid
This calculator calculates the area of a trapezoid given two parallel sides and the height.
For the calculation, enter the lengths of the two parallel sides a and c, as well as the height h. Then click on the 'Calculate' button.
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Formulas for calculating the area
The area of a trapezoid is calculated using the following formula:
\(\displaystyle A =\frac{a+c}{2} · h \)
The following graphic shows the derivation of the formula.
The trapezoid is first doubled, then the second trapezoid is rotated 180 ° and attached to the first. We get a parallelogram that has twice the area of the trapezoid. Therefore, in the formula (a + c) is divided by 2.
Then the slope is cut off on the right side ...
... and added to the slope on the left.
This creates a rectangle that has twice the area of the trapezoid. The formula results:
\(\displaystyle A =\frac{Länge · Höhe}{2} =\frac{(a+c) · h}{2} \)
Calculate area per height and center line
Alternatively, if the length of the center line is known, the following formula can be used:
\(\displaystyle A = m · h \)
The length of the center line corresponds to:
\(\displaystyle m =\frac{a+c}{2} \)
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