The formula for the area of a trapezoid is Area = a+b / 2 x H
where a and b are the length os the bases.
Filling in the information given we can solve for the missing height:
76 = (12+7) /2 x H
76 = 19/2x H
76 = 9.5 x H
H = 76/ 9.5
H = 8
The height is 8 inches.