SOLUTION: What is the area of an equilateral triangle whose perimeter is 28 in?

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Question 955043: What is the area of an equilateral triangle whose perimeter is 28 in?
Found 3 solutions by Valerie2623, Fombitz, Alan3354:
Answer by Valerie2623(1) About Me  (Show Source):
You can put this solution on YOUR website!
A= 37.72 inches^2

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You can calculate the height of the triangle,
S%5E2=%28S%2F2%29%5E2%2BH%5E2
%2828%2F3%29%5E2=%28%281%2F2%29%2828%2F3%29%29%5E2%2BH%5E2
H%5E2=%2828%5E2-28%5E2%2F4%29%2F3%5E2
H%5E2=%283%2F4%29%2828%2F3%29%5E2
H=%28sqrt%283%29%2F2%29%2828%2F3%29
So then the area is,
A=%281%2F2%29%2828%2F3%29%28sqrt%283%29%2F2%29%2828%2F3%29
A=%28196%2F9%29sqrt%283%29in%5E2

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
What is the area of an equilateral triangle whose perimeter is 28 in?
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For any regular polygon with n sides of length s:
Area+=+ns%5E2%2Acot%28180%2Fn%29%2F4
= 3%2A%2828%2F3%29%5E2%2Asqrt%283%29%2F12
%2828%2F3%29%5E2%2Asqrt%283%29%2F4
= 196%2Asqrt%283%29%2F9
=~ 37.72 sq inches