Answer:
The area of the regular hexagon is [tex]166.3\ units^{2}[/tex]
Step-by-step explanation:
we know that
The regular hexagon can be divided into 6 equilateral triangles
so In this problem
The radius is equal to length side of the polygon
The area of the regular hexagon is equal to the area of six equilateral triangle
[tex]A=6[\frac{1}{2}(b)(h)][/tex]
we have
[tex]b=r=8\ units[/tex] ---> the base of each triangle is equal to the radius
[tex]h=4\sqrt{3}\ units[/tex] ---> the height of each triangle is equal to the apothem
substitute
[tex]A=6[\frac{1}{2}(8)(4\sqrt{3})]=96\sqrt{3}\ units^{2}[/tex]
[tex]96\sqrt{3}=166.3\ units^{2}[/tex]
