Answer: [tex]36.5\ cm^2[/tex]
Step-by-step explanation:
You know that both figures are similar. So, in order to find the missing area, you need to follow these steps:
1. You must find the scale factor of the the perimeter of the smaller figure to the perimeter of larger figure. This is the ratio between the perimeters. Since it is a lenght, you know that:
[tex]scale\ factor\ perimeter=\frac{28}{20}=\frac{7}{5}[/tex]
2. Now, you must find the scale factor of the area of the smaller figure to the area of the larger figure. This is:
[tex]scale\ factor\ area=(\frac{7}{5})^2=\frac{49}{25}[/tex]
3. Set up the following proportion:
[tex]\frac{49}{25}=\frac{A}{18.6}[/tex]
4. Finally, you must solve for "A", which is the area of the larger figure:
[tex](18.6)(\frac{49}{25})=A\\\\A=36.5\ cm^2[/tex]
