What is the area of a hexagon with an apothem of 4 square root 3 ?

A hexagon is six equilateral triangles; the apothem is the height of one of them.

The right triangle associated with that apothem has sides in ratio so the hypotenuse, which is the side of the equilateral triangle, is

so an area of a single triangle

The entire hexagon is six of these

hope it you

step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2