Answer:
The area of the larger octagon is  [tex]236.18\ in^2[/tex]
Step-by-step explanation:
The question is
What is the area of the larger octagon?
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
so
Let
z ----> the scale factor
x ----> the area of the larger octagon
y ---> the area of the smaller octagon
[tex]z^2=\frac{x}{y}[/tex]
we have that
[tex]z=3.5[/tex]
Because, in similar figures the ratio of corresponding sides is proportional and this ratio is equal to the scale factor
we have
[tex]z=3.5[/tex]
[tex]y=19.28\ in^2[/tex]
substitute the given values
[tex]3.5^2=\frac{x}{19.28}[/tex]
[tex]x=12.25(19.28)=236.18\ in^2[/tex]
