Question

How do you find the perimeter of a trapezoid when you only know the top length, base length, and height?

Answer 1

You can not.

Explanation:

The top length, base length, and height are not sufficient to determine the perimeter of a trapezoid
as demonstrated by the counter-example below:

Both trapezoids have the same top length, base length, and height.

If they have equal perimeters:
`color(white)("XXX")color(red)((A+1))` must be equal to `color(blue)((2B))`

By the Pythagorean Theorem
`color(white)("XXX")color(red)(A+1=sqrt(17)+1 ~= 5.123)`
and
`color(white)("XXX")color(blue)(2B=2(sqrt(5))~=4.472`

Therefore the perimeters are not equal even though the top, base and height lengths are equal.