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Ratios of Areas - Lesson 11-7

Today we looked at the ratio of areas of figures. We can start with the following example:

Ratio of Areas Example Problem

Which is pretty straight forward to answer:

Example Problem Answer

Now look at a second example:

Ratio of Areas Example Problem 2

Which is a little less straight forward, but still doable with the realization that both triangles had the same height, which then cancelled out when we did the algebra:

Answer for Example Problem 2

Next, consider the following example:

Ratio of Areas Example 3

This is interesting...all we have is similar triangles with the ratio of corresponding sides. However, that is enough information to solve the problem!

Answer for Example Problem 3

This fact turns out to hold true for all similar polygons:

Theorem 107 - Similar figures Theorem

This theorem makes problems of this sort pretty easy. Here's an example:

Ratio of Areas Example 4

and its solution!

Answer for Example Problem 4

There is one more theorem for today:

Theorem 108 - the Triangle Median Theorem

This should make sense to you if you think about it and look at the following:

Reasoning behind the Triangle Median Theorem

Other Links
Class Notes
Lesson 11-1
Lesson 11-2
Lesson 11-3
Lesson 11-4
Quiz Topics
Lesson 11-5
Lesson 11-6
Lesson 11-7
Lesson 11-8
Test Topics
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