Key property: A regular hexagon consists of 6 equilateral triangles

So we can divide the given hexagon into 6 equilateral triangles as follows:

This means, the area of the entire hexagon = the area of 6 equilateral triangles

We'll now label the four portions that comprise the shaded area as follows:


So....
The area of region A = 1/2 of an equilateral triangle
The area of region B = 1/2 of an equilateral triangle
The area of region C = 1/2 of an equilateral triangle
The area of region D = 1/2 of an equilateral triangle

So, the total shaded area = (1/2) + (1/2) + (1/2) + (1/2)
= 2

So, the shaded area is equal to the area of 2 equilateral triangles.
Since the hexagon consists of 6 equilateral triangles, the shaded portion = 2/6 of the entire hexagon.
So, if the hexagon has an area of x, the area of the shaded portion = 2/6 of x = 1/3 of x = x/3

Answer: C