AE= sqrt(17^2 + 30^2) =
\(AE=\sqrt{17^2+30^2}\\ AE= \sqrt{1189}\;cm\\~\\ EC=\sqrt{13^2+13^2}\\ EC=\sqrt{338}\;cm\\~\\ AC=\sqrt{17^2+4^2}\\ AC=\sqrt{305}\\ \)
Heron's formula for finding area.
Let a,b,c be the lengths of the sides of a triangle. The area is given by:
\(area=\sqrt{p(p-a)(p-b)(p-c)}\qquad \text{where p=half the perimeter}\\~\\ p=\frac{\sqrt{1189}+\sqrt{338}+\sqrt{305}}{2}\\~\\ \)
You can do the substitutions to find the answer.