SOLUTION: The area of a circle circumscribing about an equilateral triangle is 254.47 square meter.What is the area of the triangle in square meter?

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Question 158558: The area of a circle circumscribing about an equilateral triangle is 254.47 square meter.What is the area of the triangle in square meter?
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
Remember:
Area%5Bet%5D=s%5E2sqrt%283%29%2F4 -------------------> eqn 1
The sides=s are unknown? But remember the formula for circumscribed circle radius------> r=s%2Asqrt%283%29%2F3 ------> eqn 2
The radius=r is unknown? But Area%5Bc%5D is given so we can get r:
A%5Bc%5D=pi%2Ar%5E2
254.47=pi%2Ar%5E2
%28254.47%2Fpi%29=cross%28pi%29%2Ar%5E2%2Fcross%28pi%29
r=sqrt%28254.47%2Fpi%29
r=9meters
Go back eqn 2:
9=s%2Asqrt%283%29%2F3
%289%2A3%29%2Fsqrt%283%29=s
s=27%2Fsqrt%283%29 , substitute in eqn 1
A%5Bet%5D=%2827%2Fsqrt%283%29%29%5E2%2Asqrt%283%29%2F4
A%5Bet%5D=%28729%2F3%29%2Asqrt%283%29%2F4
A%5Bet%5D=243%2Asqrt%283%29%2F4=105.22m%5E2, FINAL ANSWER
.Note: see www.mathwords.com
Thank you,
Jojo