Final answer:
To determine the area of Polygon Q and the scale factor used, we need the area of Polygon Q. The ratio of the areas gives us the square of the scale factor; taking the square root gives the actual scale factor.
Step-by-step explanation:
To find out how many times larger the area of Polygon Q is compared to the area of the original Polygon P, we need to know the scale factor that Noah applied. Since the area of Polygon P is 5 square units, we can use the fact that the area of similar polygons scales by the square of the scale factor.
If we knew the area of Polygon Q, we would take the ratio of the area of Polygon Q to the area of Polygon P and then find the square root of that ratio to determine the scale factor. For example, if the area of Polygon Q was 20 square units, then Polygon Q would be 4 times larger than Polygon P because 20 divided by 5 equals 4. The scale factor in this case would be √4, which is 2, meaning each length in Polygon P was multiplied by 2 to create Polygon Q.
Without the specific area of Polygon Q, we cannot determine the exact scale factor that Noah applied. However, using another example, if Noah drew a Polygon Q with each side length twice as long as those in Polygon P, then the scale factor would indeed be 2, resulting in an area 4 times larger (since area scales by the square of the scale factor).