What is the area, rounded to the nearest tenth of square inch, of an equilateral triangle that has a perimeter of 24 inches?

Answer: 27.7 square inches.Step-by-step explanation:Let 'a' be the side of equilateral triangle.Then the perimeter of the triangle = a+a+a=3aGiven: Perimeter of the equilateral triangle = 24 inches[tex]\\\Rightarrow3a=24\\\\\Rightarrow\ a=8\ inches[/tex]We know that the area of a equilateral triangle is given by :-[tex]A=\dfrac{\sqrt{3} a^2}{4}\\\\\Rightarrow\ A=\dfrac{\sqrt{3} (8)^2}{4}\\\\\Rightarrow\ A=27.71281292\approx27.7\ in.^2[/tex]