Question

PLEASE HELP!!!!!!!!!!!!!!!!!

Answer 1

For any regular polygon, the area can be expressed in terms of its apothem $a$ and its perimeter $p$  like this:

$A =\frac{ap}{2}$

For the problem the apothem $a=4\sqrt{3}$

So we need to find the perimeter. A regular hexagon is built up by equilateral triangles, so the radius is equal to each side, therefore the perimeter is given by:

$p=6r=6(8)=48$

Finally, if we substitute in the first equation:

$A =\frac{4\sqrt{3}\times 48}{2}=166.27$