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Sagot :
The area of any shape after dilation is equal to the area of the original shape multiplied by the square of the scale factor:
[tex]A_{\text{new}}=k^2\cdot A_{\text{original}}[/tex]Where
A_new indicates the area of the shape after the dilation
A_original is the area of the original shape
k is the scale factor
The first step is to determine the area of the original shape and the new shape, using the formula:
[tex]A=w\cdot l[/tex]The original shape has dimensions 4 and 5, so its area is:
[tex]\begin{gathered} A_{\text{original}}=4\cdot5 \\ A_{\text{original}}=20 \end{gathered}[/tex]Next is to determine the area of the shape after the dilation (A_new)
The scale factor is k=1.2
[tex]\begin{gathered} A_{\text{new}}=k^2\cdot A_{\text{original}} \\ A_{\text{new}}=(1.2)^2\cdot20 \\ A_{\text{new}}=1.44\cdot20 \\ A_{\text{new}}=28.8 \end{gathered}[/tex]Now that we calculated both areas, we can determine the increase percentage.
- First, calculate the increase (I), which is the difference between the area of the new shape and the area of the original shape:
[tex]\begin{gathered} I=A_{\text{new}}-A_{\text{original}} \\ I=28.8-20 \\ I=8.8 \end{gathered}[/tex]-Second, divide the increase by the original area and multiply the result by 100
[tex]\begin{gathered} \frac{I}{A_{\text{original}}}\cdot100 \\ \frac{8.8}{20}\cdot100 \\ 0.44\cdot100=44 \end{gathered}[/tex]This means that the area increased 44% after the dilation
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