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 3. what is the area of figure 2? explain how you know.

Explanation:

Step1: Recall area - scale - factor relationship

The ratio of the areas of two similar figures is equal to the square of the scale - factor. Let the scale - factor from figure 1 to figure 2 be $k$. The formula for the relationship between the areas $A_1$ and $A_2$ of two similar figures is $\frac{A_2}{A_1}=k^{2}$.

Step2: Identify given values

We know that $A_1 = 20$ square units and $k = 3$.

Step3: Calculate the area of figure 2

Substitute the values into the formula $\frac{A_2}{A_1}=k^{2}$. So $A_2=A_1\times k^{2}$. Plugging in $A_1 = 20$ and $k = 3$, we get $A_2=20\times3^{2}$.
$A_2=20\times9 = 180$ square units.

Answer:

180 square units