SAT Rectangle Area Question

Date: 04/23/2004 at 18:24:55
From: Max
Subject: SAT rectangle

In rectangle ABCD, Point E is the midpoint of side BC.  If the area of 
quadrilateral ABED is 2/3, what is the area of rectangle ABCD?

I drew the rectangle out, made 2/3 into a decimal of .66, figured the 
other part of the triangle is 1/3 but don't know where to go from 
there.

Date: 04/24/2004 at 20:05:50
From: Doctor Justin
Subject: Re: SAT rectangle

Hi Max,

When working on the SAT, never make assumptions.  The test makers 
_want_ you to make assumptions in an effort to trick you!

Try drawing rectangle ABCD and point E at the midpoint of side BC.  
Now draw a line parallel to the bases from point E to side AD, 
intersecting AD at point Q.  Next, draw a line from point Q to point 
B and another from point D to point E.  We now have four congruent
triangles--can you see why?

The diagram shows that ABED contains 3 of the 4 triangles in ABCD.  
Therefore, 3/4 the area of ABCD is the area of ABED.  In other words, 
3/4*(area of ABCD) = 2/3.  Thus, (area of ABCD) = 8/9.

Does that help?  If not, please write back.

- Doctor Justin, The Math Forum
  http://mathforum.org/dr.math/