SOLUTION: Find the area of an equilateral triangle (regular 3-gon) with the given measurement. 6-inch radius A = sq. in.

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Question 279226: Find the area of an equilateral triangle (regular 3-gon) with the given measurement.
6-inch radius
A = sq. in.
Answer by CharlesG2(828) About Me  (Show Source):
You can put this solution on YOUR website!
Find the area of an equilateral triangle (regular 3-gon) with the given measurement.
6-inch radius
from http://www.mathopenref.com/polygonregulararea.html:
If you know the radius (distance from the center to a vertex):
+area+=+%28R%5E2Nsin%282pi%2FN%29%29%2F2+
where
R is the radius (circumradius)
N is the number of sides
+pi+ is PI, approximately 3.142
SIN is the sine function calculated in radians
+sin%280%29+=+0+
+sin%28pi%2F3%29+=++sqrt%283%29%2F2+
+sin%28pi%2F2%29+=+1+
+sin%282%2Api%2F3%29+=+sqrt%283%29%2F2+
+sin%28pi%29+=+0+
+area+=+%286%5E2+%2A+3+%2A+sin%282%2F3+%2A+pi%29%29%2F2+
+area+=+%2836+%2A+3+%2A+sqrt%283%29%2F2%29%2F2+
+area+=+18+%2A+3+%2A+sqrt%283%29+%2A+1%2F2+
+area+=+9+%2A+3+%2A+sqrt%283%29+
+area+=+27+%2A+sqrt%283%29+
+area+=+approximately+46.7654+square+inches++