Test 8 Section 9 - #16 (page 861)

Tough one, right?  Let's start by drawing it:

So the area of ABED is 2/3. We don't have an equation for the area of a shape like that, so let's see if draw a few more lines and see if anything becomes more clear. I'm gonna draw a few more segments, and name another point, P, which is the midpoint of AD.

Alright, now we're doing it. Notice that ABED, which we know, is 3/4 of ABCD, which we want.

ABED, which has an area of 2/3, is 3/4 of what we want. Confusing, right? At this point, you can mess with the fractions*, or you can backsolve. Look at the choices. 3/4 of one of them is going to be 2/3.

Of course, when we backsolve, we start with (C):

(C) (8/9)(3/4) = 24/36 = 2/3. 

Nice. Done already. :)

* To "mess with" the fractions, divide 2/3 by 3/4. You get 8/9.