SOLUTION: How can you find the area and perimeter of a regular triangle with only the apothem given. Or at least the line from the top to the center, I think thats what its called. In the ca

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Question 141090: How can you find the area and perimeter of a regular triangle with only the apothem given. Or at least the line from the top to the center, I think thats what its called. In the case of the problem, the length is ten.
Answer by vleith(2517) About Me  (Show Source):
You can put this solution on YOUR website!
The line you have runs from the vertex of one triangle to the opposite side correct?
Since the triangle is regular (equilateral) all 3 sides are the same length. The line from the vertex to the center of the opposite side creates a right triangle with sides 10, x, x/2 . Where x is the hypotenuse.
So use the Pythagorean theorem to solve for x
x%5E2+=+%28x%2F2%29%5E2+%2B+10%5E2
x%5E2+=+x%5E2%2F4+%2B+100
%283x%5E2%29%2F4+=+100
x%5E2+=+400%2F3
x+=+11.55+
Area = b*h = 11.55*10 = 115.5
Perimeter = 3*b = 34.65
Is that what you get ?