Associated Topics || Dr. Math Home || Search Dr. Math

### Ratio of Areas of Triangle and Parallelogram

```
Date: 7/17/96 at 1:55:27
From: Anonymous
Subject: Ratio of Triangle, Parallelogram Areas

Hi,

Can you give me some help with this problem?

In the diagram, we have BC||DF, DE||AC, BE=5, and EC=3

/\A
/   \
D/-------\F
/ \        \
/    \       \
/      \        \
B---------E--------C

Compute the Fraction:

--------------------------
Area of parallelogram DECF

```

```
Date: 7/17/96 at 10:37:53
From: Doctor Anthony
Subject: Re: Ratio of Triangle, Parallelogram Areas

similar triangles are proportional to the squares of corresponding
sides.

DBE/FEC = 5/3  This is because these triangles have equal heights, so
the ratio of the areas is the same as the ratio of their bases.

Now DECF = 2*FEC so DBE/DECF = 5/6  We now have the chain of ratios

ADF/DBE * DBE/DECF = 9/25 * 5/6 = 3/10

-Doctor Anthony,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Geometry
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