Geometry question.

Hi kamalakarthi,

I'm going to give you some hints so that you can retry this question on your own:

[spoiler]
1) When the GMAT gives you a 'weird' shape to work with, you should look for any opportunity to 'break down' that shape into shapes that you DO know. Here, you can break each parallelogram down into 2 right triangles and a rectangle.
2) Knowing those 60 degree angles, try breaking down each shape into a 30/60/90 right triangle and a rectangle. What would the sides of the triangle be? Use that information to figure out the dimensions of the rectangle.
3) When you have the area of one parallelogram, you just have to multiply that number by 3 to get the total area of all of the shapes.
[/spoiler]

GMAT assassins aren't born, they're made,
Rich

If each line segment is equal to 4, then the figure is composed of three RHOMBUSES (rhombi? I never know how to pluralize that)

Here is the figure closer to scale:


If each angle is 60 degrees, then each of these shapes can be cut into 2 equilateral triangles:



Simply find the area of an equilateral triangle with a side length of 4:



An equilateral triangle can be chopped into two 30-60-90 triangles. The height = (half of the side length of the equilateral)(sqrt 3)

So the area of the equilateral = (1/2)bh = (1/2)(4)(2√3) = 4√3

Multiply this number by 2 to get the area of each rhombus, then multiply be 3 to get the area of all the shaded figures:
(4√3)(2)(3) = 24√3

The answer is E.