The lateral area of a cone with slant height s, and radius x (as shown in the diagram), is:
[tex]A=\pi rs[/tex]Since the radius of the base is 4in and the slant height is 11in, then:
[tex]\begin{gathered} A=\pi(4in)(11in) \\ =44\pi in^2 \\ =44(3.14)in^2 \\ =138.16in^2 \end{gathered}[/tex]Therefore, the lateral area of such a hat, is:
[tex]138.16in^2[/tex]