The correct option is D 32
Each side is 4a. We can see that the area of the equilateral triangle is
twice the area of a smaller right triangles. The right triangle's area
is 1/2 base x height, and the height (b) is obtained through Pythagorus'
Theorem from the other two sides. If we put that all together, we get:
Now let's look at the hexagon. You are right that it is made up of six equilateral triangles, so each side is 2a this time:
Using the same logic as before, let's calculate the area of each small equilateral
We can see by this that the ratio of At is not half of AT it is 14 instead.Now when we look at the ratio of the area of the hexagon to the area of the large triangle, we get: