Cutting Hexagons

Further partition the hexagon into 6 identical regular triangles as shown. Clearly, the perimeter of the quatrilateral is equal to 5 times the side length of a triangle. Hence the side length of the triangle is 1. The perimeter of the hexagon is 6 times the side length of the triangle, which is 6.

If we cut the regular hexagon into 2 congruent trapezoids, then we get the formula, $\displaystyle A = \frac { u + d } { 2 } \times h$ . $u$ means the upper side, $d$ means down sides, and $h$ means the height of the trapezoid. we have to cut the trapezoid into 3 congruent regular triangles, then we get 6 congruent regular triangles, so the length of the perimeter of the regular triangle is $3$ . Then, the length of one side of the triangle is $1$ . So we can get the perimeter of the regular hexagon is $\boxed { 6 }$ .