Question

polygon c has an area of 40 square units. kennan drew a scaled version of polygon c using a scale factor of \\( \frac { 1 } { 2 } \\) and labeled it polygon d. what is the area of polygon d? square units

Explanation:

Step1: Recall the area - scale factor relationship

When a figure is scaled by a scale factor \(k\), the area of the new figure is \(k^{2}\) times the area of the original figure. Here, the scale factor \(k=\frac{1}{2}\).

Step2: Calculate the area of Polygon \(D\)

Let \(A_{C}\) be the area of Polygon \(C\) and \(A_{D}\) be the area of Polygon \(D\). We know that \(A_{D}=k^{2}\times A_{C}\). Substitute \(k = \frac{1}{2}\) and \(A_{C}=40\) into the formula. Then \(A_{D}=(\frac{1}{2})^{2}\times40\).
Since \((\frac{1}{2})^{2}=\frac{1}{4}\), we have \(A_{D}=\frac{1}{4}\times40\).

$$A_{D}=\frac{40}{4}=10$$

Answer:

\(10\)