Questions on Geometry: Polygons answered by real tutors!

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Question 145726: i want to know how you find the area of an equilateral triangle (regular 3-gon) with the given measurement.
6-inch side.
A = sq. in.: i want to know how you find the area of an equilateral triangle (regular 3-gon) with the given measurement.
6-inch side.
A = sq. in.
Answer by Earlsdon(3748) About Me  (Show Source):
You can put this solution on YOUR website!
You can use Heron's formula for finding the area of any triangle when you know only the lengths of the three sides.
Heron's formula is:
A = sqrt(s(s-a)(s-b)(s-c)) where s = the semi-perimeter of the triangle and a, b, and c are the lengths of the three sides.
In your problem, s = (6+6+6)/2 = 18/2 = 9 and a, b, and c = 6 inches each.
A = sqrt(9(9-6)(9-6)(9-6))
A = sqrt(9*3*3*3)
A = sqrt(9*27)
A = sqrt(243)
A = 15.6sq.in. to the nearest tenth.