Posted by Ivan on Sunday, January 16, 2011 at 12:44am.
There is a formula for the area of a triangle in terms of the side lengths.
Don't ask me to derive it. Here it is:
Let s = (a +b +c)/2
a,b and c are the side lengths.
For your triangle, s = 24
Area = sqrt[s*(s-a)*(s-b)*(s-c)]
= sqrt[24*9*9*6) = 108 square units
Check: Your triangle is isosceles and if you drop a line from the apex to the middle of the base, you have two
9:12:15 right triangles. The area of each is (1/2)(9*12) and that makes a total area of 108.
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