Answer: [tex]48.5\ ft[/tex]
Step-by-step explanation:
Given
Area of the regular hexagon is [tex]169.74\ ft^2[/tex]
Length of the apothem is [tex]l=7\ ft[/tex]
Suppose the side of the hexagon is a
Hexagon can be divided into six equal triangles with same area
Area of a single triangle is
[tex]\Rightarrow A_1=\dfrac{1}{2}\times 7\times a\\\\\Rightarrow A_1=3.5a\ ft^2[/tex]
Area of hexagon will be equal to area of 6 equal area triangles
[tex]\Rightarrow 6A_1=169.74\\\Rightarrow 6\times 3.5a=169.74\\\Rightarrow a=8.08\ ft[/tex]
Perimeter of the hexagon is
[tex]\Rightarrow P=6a\\\Rightarrow P=6\times 8.08\\\Rightarrow P=48.49\approx 48.5\ ft[/tex]
Thus, the perimeter of the hexagon is [tex]48.5\ ft[/tex]
