SOLUTION: can you please help me solve(((What is the area of an equilateral triangle with perimeter 12? )))

Question 200996This question is from textbook geometry
: can you please help me solve(((What is the area of an equilateral triangle with perimeter 12? ))) This question is from textbook geometry

Found 2 solutions by rfer, RAY100:
Answer by rfer(16322) (Show Source): You can put this solution on YOUR website!
a^2+b^2=c^2 for a right triangle to find the heigth
2^2+b^2=4^2
b^2=16-4=12
b=3.46
a=lh
a=1/2*4*3.46=6.92 sq something

Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
Remember,, equilateral triangle,, sides same,,,,
.
Perimeter = sum of sides = s+s+s = 3s =12,,,,s=4
.
With s=3, we could use Herons Formula ,, but just as easy to resolve.
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Area = 1/2 * base * height
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Height is perpendicular to base, therefore c^2 = a^2 + b^2.( use rough sketch)
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in our case,,,c= 4,,,,a=2,,,,therefore c= 3.46,,,which is height
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Area = 1/2 * 4 * 3.46 = 6.93
.
Check,,,rough sketch shown height to vertex makes a 30-60-90 triangle, with sides 1 - 2 - sqrt3,,
with leg 2 and hypotenuse 4, therefore other leg is 2(sqrt3) {height},
and area is 1/2 * 4* 2sqrt3 = 4 sqrt3 = 6.93,,,ok
.

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