Question

question 14 (multiple choice worth 5 points)
(scale factor and dilation lc)
a trapezoid with an area of 36 in² is dilated with a scale factor of k = 0.7. what is the area of the new trapezoid?
73.5 in²
51.4 in²
25.2 in²
17.64 in²

Explanation:

Step1: Recall the formula for area after dilation

When a figure is dilated with a scale factor \(k\), the area of the new figure \(A_{new}\) is related to the area of the original figure \(A_{old}\) by the formula \(A_{new}=A_{old}\times k^{2}\).

Step2: Substitute the given values

We are given that \(A_{old} = 36\space in^{2}\) and \(k = 0.7\). Then \(A_{new}=36\times(0.7)^{2}\).
First, calculate \((0.7)^{2}=0.49\).
Then, \(A_{new}=36\times0.49\).
\(36\times0.49=(30 + 6)\times0.49=30\times0.49+6\times0.49=14.7+2.94 = 17.64\space in^{2}\).

Answer:

\(17.64\space in^{2}\) (the fourth option)