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Find the area of an equilateral triangle (regular 3gon) with the given measurement.
3inch radius
A = sq. in.
 2 years ago
 2 years ago
Find the area of an equilateral triangle (regular 3gon) with the given measurement. 3inch radius A = sq. in.
 2 years ago
 2 years ago

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mtbender74Best ResponseYou've already chosen the best response.0
The 3inch radius measurement they gave you is the radius of the circumscribed circle around the triangle. The good news is that there's an easy way to find the height of an equilateral triangle given this radius. The radius of the circumscribed circle of an equilateral trianlge is 2/3 the height. So, 3=(2/3)h. Solving for h, we get the height to be 9/2. We still need one more piece, though (unless you have learned trigonometric functions). We need the length of the base of the triangle. To find the base of an equilateral triangle given it's height, we multiply the height by \[2/\sqrt{3}\]So,\[(9/2)(2/\sqrt{3})=9/\sqrt{3}=3\sqrt{3}\]We can now use the A forumla for a triangle. \[A=(1/2)bh=(1/2)(3\sqrt{3})(9/2)=27\sqrt{3}/4\]
 2 years ago
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