Question

Find the area of a regular hexagon given the side length is 8 in. Leave your answer in exact form (with square root) and no decimals. (Use sq rt as the square root symbol.

Answer 1

The area of a hexagon depending on its side is given by:
 $A= \frac{3L^2}{2tan(30)}$
 Rewriting we have:
 $A= \frac{3L^2}{2 \frac{1}{\sqrt{3}}}$
 $A = \frac{3\sqrt{3}L^2}{2}$
 Substituting values we have:
 $A = \frac{3\sqrt{3}(8)^2}{2}$
 Rewriting the expression we have:
 $A = \frac{3\sqrt{3}(64)}{2}$
 $A = \frac{192\sqrt{3}}{2}$
 $A = 96\sqrt{3}$
 Answer:
 the area of a regular hexagon given the side length is 8 in is:
 $A = 96\sqrt{3}$