If two polygons are similar, then the ratio of their areas is equal to the squares of the ratios of their corresponding side lengths.
6cm^2
Practice makes perfect
We are told that the triangle shown on the diagram are similar.
In order to calculate the area of the small triangle we can use Theorem 8-2, which states the following.
Theorem 8-2
If two polygons are similar, then the ratio of their areas is equal to the squares of the ratios of their corresponding side lengths.
Let A_(small) be the area of the small triangle and A_(big) be the area of the big triangle. On the diagram, we are given the corresponding side lengths of these triangles. Calculating their ratio and then raising it to the power of 2, we can determine the ratio of the areas of the triangle.
A_(small)/A_(big)=(3/12)^2
Let's substitute A_\text{big} with 96 and calculate the area of the small triangle.
