A trapezoid has bases of 15.5 feet and 14.75 feet. If the area is 121 square feet, what is the height?

Answer 1

The area of a trapezoid is found by the formula A=1/2*h*(base 1 + base 2). You know everything but the height, so just substitute everything in and solve:
121=1/2*h*(15.5 + 14.75)
121=1/2*h*30.25
121=15.125h
8=h

Answer 2

The area is equal to the average length of the bases times the height. So

(15.5 + 14.75)/2 * height = 121
30.25/2 * height = 121
15.125 * height = 121
height = 8.