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

Algebra ->  Polygons -> SOLUTION: what is the area of an equilateral triangle(regular 3-gon) with the given measurement of 6inch side the formula is A=sq.in      Log On


   

Question 245444: what is the area of an equilateral triangle(regular 3-gon) with the given measurement of 6inch side the formula is A=sq.in
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
What is the formula for the area of a triangle? 1/2 bh=area
what is the base? 6
what is the height?
To calculate the height we have to draw a line from the center of one side to the angle opposite it forming a right triangle. With one side (the hypotenuse) =6
the one side 1/2 the side (3) and the height (h).
So we have
h^2+b^2=c^2
where c=6 and b=3
h^2+3^2=6^2
h^2+9=36
h^2=27
h=sqrt(27)
so now we go back to the equilateral triangle and use 1/2 bh
where b=6 and h=sqrt(27)
Sqrt(27)=Sqrt(9*3)=3 Sqrt(3) square inches
1/2*6*3sqrt(3)=3*3sqrt(3)=9 Sqrt(3)