How can you find the area of a trapezoid using composite figures?

Suppose the base and parallel sides of the trapezium are labelled a and b. Suppose, also, that the distance between a and b is h.

Draw a diagonal.

This will split the trapezium into one triangle whose base is the trapezium's base (a) and another upside-down triangle whose base is the trapezium's top (b).

The heights of both these triangles will be the same as the distance between the parallel sides of the trapezium (h).

The area of the first triangle is 0.5*a*h

The area of the second triangle is 0.5*b*h

So the area of the trapezium = 0.5*a*h + 0.5*b*h = 0.5*(a+b)*h