Angles of a Trapezoid

The Angles of a Trapezoid calculator computes the angles of a trapezoid based on the length of the four sides.

INSTRUCTIONS: Choose units and enter the following:

• (a) Length of Side a
• (b) Length of Side b
• (c) Length of Side c
• (d) Length of Side d

Angles of Trapezoid (A,B,C,D): The calculator returns the angles in degrees.  However, these can be automatically converted to compatible units via the pull-down menu.

The Math / Science

Trapezoid or trapezium, as it's known in the UK,  is a quadrilateral with two parallel sides, shown as the top and bottom in this diagram.  The height of a trapezoid (h) is the perpendicular distance between the two parallel sides.

This method uses Heron's formula to compute the area of the triangles sides.

The method then uses the formula for the area of a triangle, A = 1/2 * x * h, to compute the height (h).

h = 2*A / x

where:

• h = height of the triangle and therefor the trapezoid
• A = area of the triangle
• x = base of the triangle which is equal to the difference of the two parallel lines (x = b-a)

With h, sines and cosines, the angles can be computed.

Trapezoid or trapezium, as it's known in the UK,  is a quadrilateral with two parallel sides, shown as the top and bottom in this diagram.  The height of a trapezoid (h) is the perpendicular distance between the two parallel sides.

A trapezoid volume is made of four trapezoids one the sides.

Trapezoid Calculators

• Area of a Trapezoid based on top, bottom and separation
• Area of a Trapezoid based on length of 4 sides
• Height of a Trapezoid
• Angles of a Trapezoid