SOLUTION: Find the area of an equilateral triangle (regular 3-gon) with the given measurement. 9-inch perimeter A = sq. in.

Algebra ->  Polygons -> SOLUTION: Find the area of an equilateral triangle (regular 3-gon) with the given measurement. 9-inch perimeter A = sq. in.       Log On


   

Question 369006: Find the area of an equilateral triangle (regular 3-gon) with the given measurement.
9-inch perimeter
A = sq. in.

Answer by lefty4ever26(59) About Me  (Show Source):
You can put this solution on YOUR website!
An equilateral triangle means all the sides have the same length. So if the perimeter is 9 you would divide it by 3 to get each sides length.
So 9/3=3.
A of a triangle=(1/2)base*height
To find the height you would cut the triangle in half down the middle to get 2 right triangles. You will need to solve one of them to get the Vertical side.
The formula a%5E2%2Bb%5E2=c%5E2 we are looking for a so we need to rearrange the problem to get a%5E2=c%5E2-b%5E2 c is the side of your triangle equal to 3. b is the 1/2 of the other side of your triangle so (3/2) Plug into the formula and solve for a.
a%5E2=3%5E2-%283%2F2%29%5E2
a%5E2=27%2F4 , take the square root of both sides to solve for a
a=%28sqrt%2827%29%29%2F2
a=height.
SO to find area
A=%281%2F2%29%283%29%28sqrt%2827%29%29%2F2
A=3%28sqrt%2827%29%29%2F4
Simplified
A=9%28sqrt%283%29%29%2F4