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= (3L^2)/(2tan(30))`
Rewriting we have:

`A= (3L^2)/(2 (1)/(√(3)))`

`A = (3√(3)L^2)/(2)`
Substituting values we have:

`A = (3√(3)(8)^2)/(2)`
Rewriting the expression we have:

`A = (3√(3)(64))/(2)`

`A = (192√(3))/(2)`

`A = 96√(3)`
Answer:
the area of a regular hexagon given the side length is 8 in is:

`A = 96√(3)`