Answer:
[tex]A=64\sqrt{3}\ cm^2[/tex]
Step-by-step explanation:
we know that
An equilateral triangle has three equal sides and three equal interior angles (each interior angle measure 60 degrees)
so
The perimeter is equal to
[tex]P=3b[/tex]
where
b is the length side of the equilateral triangle
we have
[tex]P=48\ cm[/tex]
substitute
[tex]48=3b[/tex]
solve for b
[tex]b=48/3\\b=16\ cm[/tex]
Find the area
The formula of area applying the law of sines is equal to
[tex]A=\frac{1}{2}b^2sin(60^o)[/tex]
substitute the value of b
[tex]A=\frac{1}{2}(16)^2sin(60^o)[/tex]
[tex]sin(60^o)=\frac{\sqrt{3}}{2}[/tex]
[tex]A=\frac{1}{2}(16)^2(\frac{\sqrt{3}}{2})[/tex]
[tex]A=64\sqrt{3}\ cm^2[/tex]
