Use the formula for the area of a regular polygon with nn sides with length ss and apothem a:

\(\displaystyle{A}=\frac{{1}}{{2}}{a}{n}{s}\)

Substitute \(A=816.4 ft^2\), n=8, and s=13 ft: \(\displaystyle{816.4}=\frac{{1}}{{2}}{\left({a}\right)}{\left({8}\right)}{\left({13}\right)}\)

816.4=52a

15.7=a

So, the length of the apothem is 15.7 ft.