A regular hexagon has 6 sides, each with the same length. So a perimeter of 6 means each side of this hexagon is 6 long. The sum of the internal angles of a hexagon is 180(

*n* – 2)°, where

*n* = 6, so 720°. Each interior angle of the hexagon is 720/6 = 120°. This hexagon can be split into 6 equilateral triangles, as shown.

You might have memorized that the height of an equilateral triangle is

times the side length of the triangle, which would be

for an equilateral triangle with side length 6. If not, you can derive this result with a little knowledge of 30°– 60°– 90° triangles, two of which can be made within an equilateral triangle. The sides of a 30°–60°– 90° triangle are in the ratio

, so if 2

*x* = 6, the multiplier

*x* is 3, and the height (which is the medium side of the 30°– 60°– 90° triangle) is

.

Each equilateral triangle has area of

.

The hexagon consists of 6 of these triangles, so the hexagon has an area of

.

The correct answer is D.