Question

these two triangles are scaled copies of one another. the area of the smaller triangle is 9 square units. what is the area of the larger triangle? explain or show how you know.

Explanation:

Step1: Find the scale - factor

The ratio of the corresponding side lengths of the two similar triangles is $\frac{6}{3}=2$. This is the scale - factor $k$.

Step2: Use the relationship between areas of similar figures

The ratio of the areas of two similar figures is equal to the square of the scale - factor. Let $A_1$ be the area of the smaller triangle and $A_2$ be the area of the larger triangle. Then $\frac{A_2}{A_1}=k^{2}$.
We know $A_1 = 9$ and $k = 2$, so $A_2=A_1\times k^{2}$.

Step3: Calculate the area of the larger triangle

$A_2=9\times2^{2}=9\times4 = 36$ square units.

Answer:

36 square units