Angle of a trapezoid

This function calculates the angles of a trapezoid, given is a side length and the height. To calculate the angles, enter a side length and height, then click the 'Calculate' button

The angles \( α \) and \(δ\) can be calculated with the height and the side (d), or the angles \(β\) and \(γ\) with the height and side (b).

Get angle of a trapezoid   What should be calculated ? Angle \(α\) and \(δ\) Angle \(β\) and \(γ\)  Input Delete Entries Height (h) Side (\(d\)) Side (\(b\)) Decimal places 0 1 2 3 4 6 8 10  Results Angle (\(α\)) Angle (\(β\)) Angle (\(δ\)) Angle (\(γ\))

Formula for the angle of a trapezoid

Angle Alpha \(α\)

\(\displaystyle α = asin\left(\frac{h}{d}\right)\)     \(\displaystyle = 180 - δ\)

Angle Beta \(β\)

\(\displaystyle β = asin\left(\frac{h}{b}\right)\)     \(\displaystyle β = 180 - γ\)

Angle Gamma \(γ\)

\(\displaystyle γ = 180 - β\)

Angle Delta \(δ\)

\(\displaystyle δ = 180 - α\)

Additional Information

A trapezoid is a quadrilateral with four sides. Additionally, since a trapezoid has a pair of parallel sides, there's the extra condition that the pair of angles along one of the legs are supplementary angles, meaning their sum must be 180 degrees (or π radians). The sum of all angles in a trapezoid is 360 degrees (or 2π radians).

Knowing the angles of a trapezoid is useful for identifying its height, which, in turn, helps calculate the area of the trapezoid.

The trapezoid angle calculator above can help you determine the angles when you give the height of the trapezoid and the length of a leg.

To calculate the other parameters you will find various trapezoid calculators on the next pages.