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.

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Hi. I'm Steven. This is my solution for the problem of the month.

Rectangles, squares, and parallelograms are all trapezoids because they have 1 pair of sides parallel, so they have the same formula for area.That leaves the trapezoid and the triangle to worry about.

For the formulas, h=height, b=base and t=top.

The formula for the trapezoid can then be changed:

  th+((b-t)h/2)
= th+half h(b-t)
= th+half bh-half th
= half th+half bh
= half h(t+b)

This formula also works for a triangle.

This is the answer. half height(top+bottom)