SOLUTION: Find the area of an equilateral triangle (regular 3-gon) with the given measurement. 3-inch radius A=sq.in.

Algebra ->  Polygons -> SOLUTION: Find the area of an equilateral triangle (regular 3-gon) with the given measurement. 3-inch radius A=sq.in.      Log On


   

Question 434150: Find the area of an equilateral triangle (regular 3-gon) with the given measurement.
3-inch radius
A=sq.in.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
If you know the radius (distance from the center to a vertex):
+A+=+%28r%5E2%2An%2Asin%282pi%2Fn%29%29%2F2+
where r+ is the radius and n is the number of sides
+pi+ is Pi, approximately 3.142
the sine function calculated in radians and you need

+sin%282%2Api%2F3%29+=+sqrt%283%29%2F2+=0.866
so, area A will be:
+A=+%283%5E2+%2A+3+%2A+sin%282%2F3+%2A+pi%29%29%2F2+
+A+=+%289+%2A+3+%280.866%29%2F2+%29
+A+=+%2827%2A0.866%29%2F2+%29
+A+=%2823.38%2F2%29+
A+=+11.69in%5E2