Write a single formula for area that will work for a rectangle, a parallelogram, a trapezoid, a triangle, and a square. Explain how it works.

Trapezoids

With a trapezoid's formula you have to use a diagram. You cut off the two ends of the shape making two triangles. Or b-a. Put the two triangles together to make one bigger triangle. The base is b-a. Work out the formula of that triangle with the triangle formula (1/2bh). Now we work out the rest of the trapezoids area. As you notice it is a rectangle and all you have to do is use the rectangle formula (bh). Add the two results and hey presto the formula for a trapezoid. This is the formula I just made up then: (b-a)1/2h+(ah). Or, in short, 1/2h(a=b).

Triangles

Since the measurement for a is 0 you can see how the formula works with a few changes in it: 1/2h(a+b) = 1/2h(0+b) = 1/2hb.

Squares

I made these two formulas work out the same answer:1/2h(a+b) = ab.

Rectangles

These two formulas are the same: 1/2h(a+b) = ab.

A parallelogram is the same as a rectangle, as you can see by the diagram. You cut off one end of the parallelogram and stick it on the other end.

sawdavid@freoshs.wa.edu.au