Question

polgon b is a scaled copy of polygon a using a scale factor of 5. polygon as area is what fraction of polygon bs area? a $\frac{1}{5}$ b $\frac{25}{5}$ c $\frac{1}{25}$ d $\frac{1}{10}$

Explanation:

Step1: Recall area - scale - factor relationship

The ratio of the areas of two similar polygons is equal to the square of the scale - factor. If the scale factor from Polygon A to Polygon B is \(k = 5\), and let the area of Polygon A be \(A_{A}\) and the area of Polygon B be \(A_{B}\), then \(\frac{A_{B}}{A_{A}}=k^{2}\).

Step2: Find the ratio of \(A_{A}\) to \(A_{B}\)

We know \(\frac{A_{B}}{A_{A}} = 5^{2}=25\), so \(\frac{A_{A}}{A_{B}}=\frac{1}{25}\).

Answer:

C. \(\frac{1}{25}\)