Question

polygon q is a scaled copy of polygon p using a scale factor of \frac{1}{2}. polygon qs area is what fraction of polygon ps area?

Explanation:

Step1: Recall the area - scale factor relationship

If the scale factor of two similar polygons is \(k\), the ratio of their areas is \(k^{2}\). Here, the scale factor \(k=\frac{1}{2}\).

Step2: Calculate the ratio of the areas

We use the formula \(A_{Q}/A_{P}=k^{2}\). Substitute \(k = \frac{1}{2}\) into the formula: \(A_{Q}/A_{P}=(\frac{1}{2})^{2}\).

$$(\frac{1}{2})^{2}=\frac{1\times1}{2\times2}=\frac{1}{4}$$

Answer:

\(\frac{1}{4}\)