How do you find the area of an equilateral triangle

Asked by admin @ in Mathematics viewed by 265 People

Find the area of an equilateral triangle with radius 4 sqrt 3m. Leave your answer in simpliest radical form.

Answered by admin @


Correct answer is 36\sqrt{3}

The radius of an equilateral triangle is equal to 2/3 of the height.

R= \frac{2}{3} h= \frac{2}{3} \frac{a \sqrt{3} }{2} = \frac{a \sqrt{3} }{3} 
\\4 \sqrt{3}= \frac{a \sqrt{3} }{3} 
\\3\times 4\sqrt{3}=a \sqrt{3} 
\\a=12
\\
\\A= \frac{a^2 \sqrt{3} }{4} =\frac{12^2 \sqrt{3} }{4} =\frac{144 \sqrt{3} }{4} =36 \sqrt{3} 


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