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.

Untitled_1 2

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!



3 + 4.5 = 7.5

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