What is the area of this regular hexagon?

The area is approximately ##86.6 "cm"^2##.

As this hexagon is regular, you can divide it into ##6## triangles.

Please note that all those triangles are isosceles. All angles of the hexagon are ##120°##.

As you see in the picture, each of those 6 "big" triangles can be divided into two small triangles with the angles ##30°##, ##60°## and ##90°##, and we know the length of one of the sides: ##a = 5 cm##.

To compute the area of the small right angle triangle, you need just the length of ##b##.

This you can do with ##tan##:

##tan (30°) = b/a##

##b = 5 "cm" * tan(30°) = 2.88675134595... "cm"##

This means that the area of the small right angle triangle is

##A_t = (b * a)/2 = (5 "cm" * 5 "cm" tan(30°))/2 = 25/2 tan(30°) "cm"^2 = 7.21687836487... "cm"^2##

There are ##12## equal triangles, so the area of the whole hexagon is

##A = 12 * A_t = 6 * 25 tan(30°) "cm"^2 = 86.6025403784... "cm"^2 ##

Hope that this helped!