It is a hexagon and the area given is 16 times the square root of 3

Draw a hexagon centered at origin with a "radius" of 2. Notice that each point of the hexagon makes an angle pi/3. Draw a perpendicular bisector of the central angle of one section of the hexagon. It makes a 30-60-90 right triangle with base of 1. Each section (there are 12 of them) has an area (1/2)bh = (1/2)*1*sqrt3 = (sqrt3)/2.

There are 12 so the area of this hexagon is 6 sqrt3. The area of the given hexagon is 16 sqrt3. The ratio of the areas is 8:3, so the ratios of the drawn hexagon must be factored by 8/3.

The base forming 1/12 of the perimeter is 1*(8/3) = 8/3. (8/3)(12) = 32. The perimeter is 32 and the area is given as 16 sqrt3.