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we know that
The scale factor is equal to [tex]2\frac{1}{2}[/tex]
Step 1
Convert mixed number to an improper fractions
[tex]8\frac{1}{2}\ inches=\frac{8*2+1}{2} =\frac{17}{2}\ inches[/tex]
[tex]2\frac{1}{2}=\frac{2*2+1}{2} =\frac{5}{2}[/tex]
Step 2
Increasing each dimension by the scale factor
[tex]\frac{17}{2}*\frac{5}{2}=\frac{85}{4}\ inches[/tex]
[tex]11*\frac{5}{2}=\frac{55}{2}\ inches[/tex]
Step 3
Find the area of the new poster
we know that
the area of the poster is equal to find the area of a rectangle
[tex]A=\frac{85}{4}*\frac{55}{2}=\frac{4,675}{8}\ inches^{2}[/tex]
[tex]A=584.375\ inches^{2}[/tex]
convert to mixed number
[tex]A=(584+0.375)\ inches^{2}[/tex]
[tex]A=(584+\frac{3}{8})\ inches^{2}[/tex]
[tex]A=584\frac{3}{8}\ inches^{2}[/tex]
therefore
the answer is
The area of the new poster is [tex]584\frac{3}{8}\ inches^{2}[/tex]
Alternative Method
Let
A1--------> area of the original poster
A2------> area of the new poster
sf-------> scale factor
we know that
[tex]A2=A1*(sf)^{2}[/tex]