The area os any regular polygon is given by:
[tex]A=\frac{1}{2}Pa[/tex]
where P is the perimeter and a is the apothem. The perimeter of a regular polygon is given by:
[tex]P=ns[/tex]
where n is the number of sides and s is the length of its side. In this case we have a triangle, then n=3; we also know the length of the side, plugging these values we have:
[tex]\begin{gathered} P=(3)(28\sqrt{3}) \\ P=84\sqrt{3} \end{gathered}[/tex]
Plugging the value of the perimeter and the apothem on the expression for the area we have:
[tex]\begin{gathered} A=\frac{1}{2}(84\sqrt{3})(14) \\ A=588\sqrt{3} \end{gathered}[/tex]
Therefore, the area of the triangle is:
[tex]A=588\sqrt{3}[/tex]
This is approximately 1018.4 square units
