SOLUTION: Three circles of radii 2, 4, and 6 are tangent to each other externally. Find the area of the triangle formed by connecting their centers.

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Question 388452: Three circles of radii 2, 4, and 6 are tangent to each other externally. Find
the area of the triangle formed by connecting their centers.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The lengths of the sides of the triangle are the sums of the respective radii.
a=2%2B4=6
b=2%2B6=8
c=4%2B6=10
Use Heron's formula,
A=sqrt%28s%28s-a%29%28s-b%29%28s-c%29%29
where
s=%28a%2Bb%2Bc%29%2F2
s=%286%2B8%2B10%29%2F2
s=12
Then,
A=sqrt%2812%2812-6%29%2812-8%29%2812-10%29%29
A=sqrt%2812%286%29%284%29%282%29%29
A=sqrt%28144%2A4%29
A=12%2A2
highlight%28A=24%29