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# Geometry

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Find the area of triangle ACE.

Sep 20, 2021

#1
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[ACE] = [1/2(17*30)] - (4*17/2) - (132)/2 - 4*13

Sep 21, 2021
edited by Guest  Sep 21, 2021
#2
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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.

Sep 21, 2021