If points (6,0), (0,0), (0,2), and (a,2) are consecutive vertices of a trapezoid of area 7.5, what is the value of a?

A) 1.5

B) 2

C) 2.5

D) 5

E) 9

Backsolve this. If *a* is 2.5, like choice C says, then your trapezoid looks like this:

I put the dashed line in there to make it easier to see how you can calculate the area without remembering any trapezoid area formula: just break it into a triangle and a rectangle! You’ll find that the area of that trapezoid is 8.5, which is too big. So go smaller.

Because I know I want a .5 at the end of my area, I decided to skip 2 and go straight to 1.5 for *a*. Lo and behold, that works!