Question

a pentagon with an area of 30 yd² is dilated with a scale factor of k = 1.8. what is the area of the new pentagon? 108 yd² 97.2 yd² 54 yd² 16.7 yd²

Explanation:

Step1: Recall the formula for the area of a dilated figure

The formula for the area of a dilated figure is \(A_{new}=A_{original}\times k^{2}\), where \(A_{original}\) is the area of the original figure and \(k\) is the scale factor.

Step2: Substitute the given values into the formula

Given \(A_{original} = 30\space yd^{2}\) and \(k = 1.8\). Then \(A_{new}=30\times(1.8)^{2}\).
First, calculate \((1.8)^{2}=1.8\times1.8 = 3.24\).
Then, \(A_{new}=30\times3.24\).
\(30\times3.24=(30\times3)+(30\times0.24)=90 + 7.2=97.2\space yd^{2}\).

Answer:

\(97.2\space yd^{2}\) (the second option)