The scale factor for two similar rectangles is 9. If the area of the smaller rectangle is , what is the area of the larger rectangle?
We have two similar rectangles, where the scale factor of their corresponding dimensions is 9. Let's denote the area of the smaller rectangle by \( A_{small} \). We want to find the area of the larger rectangle, \( A_{large} \).
For similar figures, the ratio of their areas is the square of the scale factor of their corresponding linear dimensions. Since the scale factor is 9, the ratio of the areas will be \( 9^2 \) or 81.
Now, we can set up a proportion to find the area of the larger rectangle:
\[
\frac{A_{large}}{A_{small}} = 9^2
\]
\[
A_{large} = A_{small} \times 9^2
\]
\[
A_{large} = A_{small} \times 81
\]
Using the given area of the smaller rectangle, \( A_{small} \), we can calculate the area of the larger rectangle by multiplying \( A_{small} \) by 81. However, you did not provide the specific area value for the smaller rectangle, so to complete this calculation, simply multiply the given area by 81 to find \( A_{large} \).