First find height using Pythagorean theorem.
[tex]h^2+4^2=13^2\implies h=\sqrt{153}\approx12.37[/tex].
Then use cone surface area formula and compute the result:
[tex]A=\pi r(r+\sqrt{h^2+r^2})\approx\boxed{68\pi}\mathrm{units^2}[/tex].
Hope this helps.
