SOLUTION: Area of a equilateral triangle with a 3 inch radius!!! Plz Help really need this

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Question 318866: Area of a equilateral triangle with a 3 inch radius!!!
Plz Help really need this

Found 2 solutions by solver91311, JBarnum:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


An equilateral triangle does not have a radius. The the term radius is exclusive to the description of a circle, being the measure from the center to any point on the circle. Now, an inscribed circle or a circumscribed circle has a radius, and if the equilateral triangle of which you speak has an inscribed circle with a radius of 3 or a circumscribed circle with a radius of 3, then we can help you calculate the area of the triangle. But you have to tell us which.


John


Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
prob best to draw the triagle to visualize an equalateral triangle meaning all sides the same the radius is 3 and also it disects the base side at a 90 degree angle and the base is seperated in 2 equal segments. so if x= the hypotenuse of the right triagle which is the same as the length of one side of the equalateral triangle then the base of the right triangle has to be %281%2F2%29x now i would do the therom a%5E2%2Bb%5E2=c%5E2 where a=6 b=(1/2)x and c=x
the hieght of the right triangle is 2*(radius) so 2*3=6


a%5E2%2Bb%5E2=c%5E2
6%5E2%2B%28x%2F2%29%5E2=x%5E2
36%2B%28x%5E2%2F4%29=x%5E2
144%2Bx%5E2=4x%5E2
144=3x%5E2 divide by 3
48=x%5E2 sqrt each side
sqrt%2848%29=x
sqrt%283%2A4%2A4%29=x
4%28sqrt%283%29%29=x


so %281%2F2%29bh=a b=base h=hieght a=area
b=4%28sqrt%283%29%29
h=6


%281%2F2%29%284%28sqrt%283%29%29%29%286%29=a
%284%28sqrt%283%29%29%29%283%29=a
highlight%2812%28sqrt%283%29%29=a%29