Answer:
166.27 m2
Step-by-step explanation:
area of hexagon = [tex]\frac{3*\sqrt{3} }{2}[/tex]*[tex]a^{2}[/tex] where a = length of 1 side
this hexagon is made of 6 equivalent triangle
consider ABC triangle
let AC length be x
AB = 2 * AC = 2x = a
[tex]bc^{2} = ab^{2} - ac^{2} \\(4\sqrt{3})^{2} =(2x)^{2} - x^{2} \\48=3*x^{2}\\ 16=x^{2} \\x=4[/tex]
Hence a = 8
hence area of hexagon = [tex]\frac{3*\sqrt{3} }{2}[/tex]*[tex]a^{2}[/tex] = [tex]\frac{3*\sqrt{3} }{2}[/tex] * [tex]8^{2}[/tex] = 166.27 m2
