How do I write the formula for a trapezoid? Using b1 and b2 for the lengths of the base, and using h for the height

The question says "Write the formula for the area A of a trapezoid. Use b1 and b2 for the lengths of the bases, and use h for the height. I used #A= (b1+b2)/2h# but it wasn't right. Is there a variant of the formula that I'm missing? Thanks!

1 Answer
Sep 6, 2017

There are several ways, but the easiest to interpret are #A=1/2(b_1+b_2)h# and #A=(b_1+b_2)/2 xx h#.

Explanation:

Mathematically, your answer of #A=(b_1+b_2)/2 h# is okay. It successfully indicates that we should take the average of the two bases and multiply this by #h#. If we gave this formula to a student who had no idea what it meant, all they would need is a basic understanding of how to interpret formulas and they would be able to use it to find the area of any trapezoid just fine.

There are better ways to express the formula, though. Much like how a sentence can be written in multiple ways to convey the same meaning, a formula can sometimes be written multiple ways and still produce the same result.

If given the opportunity to tweak the form as it is written here, I would make it visually clear that the #h# standing alone next to the fraction is a multiplicand, like this:

#A=(b_1+b_2)/2 xx h#

This removes any doubt about the operation to be performed on #h#.

You could also write the formula with the #1/2# factored out, like this:

#A=1/2(b_1+b_2)h#

This form necessitates the parentheses around #b_1+b_2#, which in turn removes the need for a #xx# sign before the #h#.

There are many other ways to write the formula, including #A=h/2(b_1+b_2)# and #A=(h(b_1+b_2))/2#, but although they produce the same output, these forms begin to hide the story behind where the formula comes from, which is that the area of a trapezoid is the product of [the average of its bases] and [its height].