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### 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/
```
Associated Topics:
High School Triangles and Other Polygons

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The text passage contains a mathematical question about the area of a rectangle and a detailed solution provided by Dr. Math.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
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### 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/
```
Associated Topics:
High School Triangles and Other Polygons

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search
user
The text passage contains a mathematical question about the area of a rectangle and a detailed solution provided by Dr. Math.

TYPE: SINGLE_QUESTION_WITH_ANSWER