# 8.9: Composite Area and Change of Dimensions

Difficulty Level: At Grade Created by: CK-12

Editor’s note: This lesson has very limited material supported by CK-12. Please refer to the Geometry Access Reader for additional materials.

## Learning Objectives

• Use similarity to generalize the results.

## Similarity

We know that all circles are similar to each other.

Suppose a circle has a radius of \begin{align*}r\end{align*} units.

• The scale factor of this circle (with radius \begin{align*}r\end{align*} ) and the circle with radius 1 is:

\begin{align*}r : 1, \quad \frac{r}{1}, \quad \text{or just} \quad r\end{align*}.

• You know how a scale factor affects area measures:

If the scale factor is \begin{align*}r\end{align*}, then the area is \begin{align*}r^2\end{align*} times as much.

1. Explain how we know that all circles are similar to each other.

(Hint: Think about similar measurements that circles may have.)

\begin{align*}{\;}\end{align*}

\begin{align*}{\;}\end{align*}

\begin{align*}{\;}\end{align*}

\begin{align*}{\;}\end{align*}

2. If the scale factor of a circle is \begin{align*}r\end{align*}, how does this relate to a circle’s area?

\begin{align*}{\;}\end{align*}

\begin{align*}{\;}\end{align*}

\begin{align*}{\;}\end{align*}

\begin{align*}{\;}\end{align*}

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