So my explanation here is:

From the figure we have 4 right triangles and 2 rectangles.
Since it is a 6 side figure using (N-2)*(180º), we have (6-2)*(180º) = 720 must be the sum of the 6 angles, xº, which means each xº = 120
Now, with that in mind:
a) The right triangles: the hypotenuse = 6 and using the properties of a right triangle since we are cutting in half the 120º we have a 60º in one corner so the last angle must be a 30º. With this we can see the property 2x: x: x*sqrt(3) -> 6: 3: 3*sqrt(3), so the area of the triangle is: (bh/2) = (3*3sqrt(3))/2 = (9/2)*sqrt(3)

b) Now we have the rectangles, which we know now from the triangles that the width is 6 and the length is 3* sqrt(3), the Area = 3 *sqrt(3) * 6 = 18 * sqrt (3)

c) we have 4 triangles and 2 rectangles to add which will give us:
(4 * (9/2) * sqrt(3)) + (2 * 18 * sqrt(3)) = 54 * sqrt(3)
So answer is A

Sorry for not being able to put an image and hopefully it helps.

Cheers