SOLUTION: Find the area of an equilateral triangle with sides 12cm each. I tried this problem three times but got a differnt awnser each time.

Algebra ->  Triangles -> SOLUTION: Find the area of an equilateral triangle with sides 12cm each. I tried this problem three times but got a differnt awnser each time.       Log On


   

Question 443981: Find the area of an equilateral triangle with sides 12cm each. I tried this problem three times but got a differnt awnser each time.
Found 2 solutions by poliphob3.14, swincher4391:
Answer by poliphob3.14(115) About Me  (Show Source):
You can put this solution on YOUR website!
To find the area you need to compute the height using Pythagorean Theorem:
h=sqrt%2812%5E2-6%5E2%29=sqrt%28108%29=6sqrt%283%29. Now we find the area
A=%281%2F2%29%2A12%2A6sqrt%283%29=36sqrt%283%29+cm%5E2

Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
Since all three sides are equilateral, the triangle is also equiangular.
You have 180 degrees in a triangle, three angles, so each angle is 60.
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If you draw a line from the top vertex to the middle of the base, you now have a height, and it divides the top angle into two 30 degree angles.
So now we have a two right triangles. Solve either one to get the height. The base,12, is cut evenly, so the base of either triangle is 6. We know that the other side is 12, and this is our hypotenuse. We have a 30,60,90 triangle. The relationship between the shortest side and middle side is sqrt%283%29. Then our height is 6%2Asqrt%283%29.
So our formula for area is A+=+%281%2F2%29%2Ab%2Ah Our base is 12, our height is 6%2Asqrt%283%29.
So
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For future reference, to check:
The area of an equilateral triangle is %28s%5E2%2Asqrt%283%29%29%2F4