Question

polygon y has an area of 11 square units. celia drew a scaled version of polygon y using a scale factor of 3 and labeled it polygon z. what is the area of polygon z? square units

Explanation:

Step1: Recall the area - scale factor relationship

When a figure is scaled by a scale factor \(k\), the ratio of the areas of the scaled figure (\(A_{Z}\)) and the original figure (\(A_{Y}\)) is \(k^{2}\). That is \(\frac{A_{Z}}{A_{Y}}=k^{2}\).

Step2: Substitute the given values

We know that \(A_{Y} = 11\) square units and \(k = 3\). Substituting into the formula \(\frac{A_{Z}}{A_{Y}}=k^{2}\), we get \(\frac{A_{Z}}{11}=3^{2}\). Since \(3^{2}=9\), the equation becomes \(A_{Z}=11\times9\).

Step3: Calculate the area of Polygon \(Z\)

\(A_{Z}=11\times9 = 99\).

Answer:

99