We have the following equation to find the lateral area of the cone:
[tex]L=\pi\cdot r\cdot\sqrt[]{r^2+h^2}[/tex]
where 'r' is the radius of the base and 'h' is the height.
In this case, we have the following:
[tex]\begin{gathered} r=\frac{d}{2}=\frac{6}{2}=3 \\ h=8 \end{gathered}[/tex]
then, using the equation above, we get:
[tex]\begin{gathered} L=(3.14)(3)\cdot\sqrt[]{(3^2+(8)^2}=9.42\cdot\sqrt[]{9+64}=9.42\cdot\sqrt[]{73}=80.48 \\ \Rightarrow L=80.48ft^2\approx81ft^2^{} \end{gathered}[/tex]
therefore, the lateral area of the cone is 80.48 ft^2
