A trapezoid with bases b and d (d > b), legs a and c, and AD and BC are parallel is shown below . Calculate all its angles and its height h.

Angles of a TrapezoidUsing the trapezoid above, we draw BB' parallel to CD. Using the triangle ABB', we use the cosine rule to write c^{2} = a^{2} + (db)^{2}  2 a (d  b) cos(?BAD) cos(?BAD) = (a^{2} + (db)^{2}  c^{2}) / (2 a (d  b) ) In the same figure, ?BB'A and ?CDA have the same size. Using the same triangle, we use the cosine rule again to write a^{2} = c^{2} + (db)^{2}  2 c (d  b) cos(?BB'A) cos(?BB'A) = (c^{2} + (db)^{2}  a^{2}) / (2 c (d  b) ) In the given trapezoid, AD and BC are parallel. Hence the pairs of angles BAD and ABC and CDA and DCB are supplementary. Hence
Height and Area of a Trapezoid
Diagonals of a TrapezoidUse cosine rule in triangles DAB and BCD to write: BD^{2} = a^{2} + d^{2}  2 a d cos (? BAD) CA^{2} = c^{2} + d^{2}  2 c d cos (? CDA)
More References and Links to GeometryGeometry Tutorials, Problems and Interactive Applets.Trapezoid Area Calculator. Calculator to calculate the area of a trapezoid given the bases and the height. Trapezoid Calculator and Solver. An easy to use online calculator to solve trapezoid problems. The area, the angles and the diagonals of a Trapezoid are calculated given its 4 sides. 