Trapezoid diagonal e calculator

This function calculates the diagonal e of a trapezoid using the lengths of the sides and an angle. For the calculation, enter the lengths of the two sides a and b and the angle β. Then click the 'Calculate' button

Formulas for calculating the diagonal e

If the height is not known, the diagonal e can also be calculated using the angle β.

\(\displaystyle e =\sqrt{(a^2+b^2) - (2 · a · b · cos(β))} \)

calculating the diagonal e using sides and height

Using side a and b

The diagonal e forms a right triangle with the height h and the side (a - y). The diagonal e that forms the hypotenuse here can be calculated according to the Pythagorean theorem.

First, the length of y has to be calculated, which in turn can be calculated from b and h :

\(\displaystyle y =\sqrt{b^2-h^2} \)

The diagonal e can now be calculated using the following formula:

\(\displaystyle e =\sqrt{(a-y)^2+h^2} \)

The formula above is also used by this online calculator.

Use of the side length c and d

Alternatively, you can calculate with the side lengths c and d . To do this, the leg of the left triangle is first calculated:

\(\displaystyle x =\sqrt{d^2-h^2} \)

In the following formula, x is added to the side length c .

\(\displaystyle e =\sqrt{(c+x)^2+h^2} \)