SAT Rectangle Area QuestionDate: 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/ |
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