Question

noah drew a scaled copy of polygon p and labeled it polygon q. if the area of polygon p is 5 square units (sq. units), what scale factor did noah apply to polygon p to create polygon q? explain or show how you know.

Explanation:

Step1: Count area of Polygon Q

By counting the grid - squares, the area of Polygon Q is 20 square units.

Step2: Recall area - scale factor relationship

The ratio of the areas of two similar polygons is equal to the square of the scale factor. Let the scale factor be $k$. Then $\frac{\text{Area of Q}}{\text{Area of P}}=k^{2}$.

Step3: Calculate scale factor

We know that $\text{Area of P} = 5$ square units and $\text{Area of Q}=20$ square units. So, $k^{2}=\frac{20}{5}=4$. Taking the square - root of both sides, since the scale factor is positive for an enlargement, $k = 2$.

Answer:

2