We know that the smaller base is x cm, the greater base is x+4 cm, and that the height is x/2 cm.
Since the area of a trapezium is given by
If we plug the expressions we have
If this must equal 84, we can solve for x as follows: start with
Multiply both sides by 4:
Subtract 336 from both sides:
We can divide both sides by 2 to make computation simpler:
Use the quadratic formula (or any mean you prefer) to solve this equation and get the solutions
We can't accept the negative solution, because it would imply
and we can't have negative side lengths. So, the answer is 12.