How do I derive the area of a trapezoid?

The area of a trapezoid is:

A = 1/2 (b1 + b2) h

Area equals half the sum of the 2 bases times the height.

--Drop perpendiculars from the short base to the long base.

That splits the trapezoid up into a rectangle and two right triangles.

- - The area of a rectangle is (length) x (width).

The area of a triangle is (1/2) (base x height).

- - Apply these area formulas to the three parts of the trapezoid,

addum up, and you'll wind up with

Area = (1/2) (height) (long base + short base)

for the total area of the trapezoid.