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