Question

1. figure 2 is a scale drawing of figure 1. the area of figure 1 is 20 square units, and the scale factor that relates figure 2 to figure 1 is $\frac{1}{2}$. what is the area of figure 2? explain how you know.

Explanation:

Step1: Recall area - scale factor relationship

If the scale factor of two similar figures is $k$, the ratio of their areas is $k^{2}$. Here, $k=\frac{1}{2}$.

Step2: Calculate the area of figure 2

Let $A_1$ be the area of figure 1 and $A_2$ be the area of figure 2. We know that $\frac{A_2}{A_1}=k^{2}$. Given $A_1 = 20$ square - units and $k=\frac{1}{2}$, then $A_2=A_1\times k^{2}$. Substitute the values: $A_2 = 20\times(\frac{1}{2})^{2}$.
\[

$$\begin{align*} A_2&=20\times\frac{1}{4}\\ & = 5 \end{align*}$$

\]

Answer:

5 square units