Geometry question, Please help

Question

Points A, B, C, D, E, and F are the verticies of a regular hexagon and also trisect the sides of the large equilateral triangles as shown. Given that the area ABCDEF is 24, what is the total area of the shaded regions?

Answer 1

Having drawn and labeled a diagram, like you should have.

The six sides of the regular hexagon are each 4 (24 / 6)

The sides of the the triangle are 12 (they have been trisected with a 4 unit side one of sections.

Since the area of the triangle and the area of hexagon are readily determined,

what is the total area of the little triangles?

The area of an equilateral triangle of side x is x²√3 / 4, in this case 4√3

What is the area of all three?