In order to calculate the area of the bigger rectangle 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 rectangle and A_(big) be the area of the big rectangle. On the diagram we are given the corresponding side lengths of these rectangles. Calculating their ratio and then raising it to the power of 2, we can determine the ratio of the areas of the rectangles.
A_(small)/A_(big)=(3/6)^2
Let's substitute A_\text{small} with 27 and calculate the area of the big rectangle.
