Question

from unit 1, lesson 6
noah drew a scaled copy of polygon p and
labeled it polygon q.
if the area of polygon p is 5 square units, what
scale factor did noah apply to polygon p to
create polygon q?
explain or show how you know.

Explanation:

Step1: Count the area of Polygon Q

By counting the unit squares in Polygon Q, we find its area is \( 45 \) square units.

Step2: Use the area - scale factor relationship

The relationship between the areas of two similar polygons (scaled copies) is \( A_{Q}=k^{2}A_{P} \), where \( k \) is the scale factor, \( A_{Q} = 45 \), and \( A_{P}=5 \).
Substitute the values into the formula: \( 45 = k^{2}\times5 \).

Step3: Solve for \( k^{2} \)

Divide both sides of the equation \( 45 = k^{2}\times5 \) by \( 5 \): \( k^{2}=\frac{45}{5}=9 \).

Step4: Solve for \( k \)

Take the square root of both sides. Since the scale factor \( k>0 \), \( k = \sqrt{9}=3 \).

Answer:

The scale factor is \( 3 \).