Question 663673
Equilateral means all the sides are the same
p = a+b+c or in this case 3s
12 = 3s
s = 4 in for each side
...
To  find the height, cut the triangle in half to create two right triangles.
The bottom of one of the triangles is 4/2 = 2
The hypotenuse of the right triangle is 4
solve for the other side, is solving for height
s^2 + 2^2 = 4^2
Isolate s^2
s^2 = 4^2 - 2^2
s^2 = 16-4 = 12
s^2 = 12
{{{sqrt(s) = sqrt(12)}}}
s = {{{sqrt(4*3)}}}
s = 2{{{sqrt(3)}}}
...
a = 1/2(b)(h)
a = 1/2(4)(2{{{sqrt(3)}}})
a = 2(2{{{sqrt(3)}}})
a = 4{{{sqrt(3)}}}
.....
Alternatively,
The area formula in an equilateral triangle is 
{{{a=(s^2sqrt(3))/(4)}}}
Plug in the side determined from the perimeter
{{{a=(4^2sqrt(3))/(4)}}}
Such that,
{{{a=4sqrt(3)}}}
.........................
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