Answer:
[tex]16\sqrt{3}\:\mathrm{units^2}[/tex]
Step-by-step explanation:
The area of an equilateral triangle with side length [tex]s[/tex] is equal to [tex]\frac{\sqrt{3}}{4}s^2[/tex]. Since the perimeter is 24 units and there are three equal sides to an equilateral triangle, each side is [tex]24\div 3=8[/tex] units.
Substituting in this value, we get:
[tex]\frac{\sqrt{3}}{4}8^2=\frac{64\sqrt{3}}{4}=\boxed{16\sqrt{3}}[/tex]
