SOLUTION: Find the area of an equilateral triangle given side length 24.

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Question 728725: Find the area of an equilateral triangle given side length 24.
Answer by ohtheirony(35) About Me  (Show Source):
You can put this solution on YOUR website!
The median and altitude are the same line in an equilateral triangle. The median divides the base into two equal parts, so 12 and 12. You can use the Pythagorean theorem to find the height. We have the hypotenuse (c=24) and the base (a=12).
So c%5E2=a%5E2%2Bb%5E2 becomes...
24%5E2=12%5E2%2Bb%5E2
576=144%2Bb%5E2
432=b%5E2
The opposite of squaring is the square root. So , we take the square root of each side.
sqrt%28432%29=sqrt%28b%5E2%29
b=20.7846096908
To find the area, multiply 1/2bh, or 1/2 the base times the height.
1/2(12)(20.7846096908)=124.707658145
Multiply this answer by two, and you will have the full equilateral triangle.
124.707658145(2)=249.41531629
area=~249.415