Suppose I have a right trapezoid with base lengths of 4 and 16. Is there any way I can find out what the missing side is? (see image attached)

  no

Step-by-step explanation:

If you draw a line from the right end of the top base to the bottom base, parallel to the left side, you cut off a right triangle that has a bottom leg of 12 and two unknown sides (height, and slant length).

All you can say is that the unknown slant length is more than 12 units.

If you know the height, you can find the slant length (hypotenuse) using the Pythagorean theorem.

well what did you do it matters what you did : )

step-by-step explanation:

yes.. it's proven to be 36.