Question

1. figure 2 is a scale drawing of figure 1. the area of figure 1 is 15 square units, and the scale factor is 5. what is the area of figure 2? explain how you know.

Explanation:

Step1: Recall area - scale - factor relationship

If the scale factor between two similar figures is $k$, the ratio of their areas is $k^{2}$.

Step2: Identify the scale factor and given area

The scale factor $k = 5$ and the area of figure 1, $A_1=15$ square units. Let the area of figure 2 be $A_2$. Then $\frac{A_2}{A_1}=k^{2}$.

Step3: Calculate the area of figure 2

Substitute $k = 5$ and $A_1 = 15$ into the formula $\frac{A_2}{A_1}=k^{2}$. We get $\frac{A_2}{15}=5^{2}=25$. Then $A_2=15\times25 = 375$ square units.

Answer:

375 square units