Finding the dimensions of scaled down triangles

Question

I am given the following equilateral triangle:

The lengths of GH & GI both equal 1 and since we know that its an equilateral triangle, we know that the angles are 60 degrees for all 3 corners. Because these are the only givens, I assumed that GP = 0.2 and PI = 0.8. These are feasible values and so I was able to work out the values for the out-most green triangles (excuse the quality). Its area turned out to be (0.08)sin60:

Right now, I am being asked to find the area of the shaded region:

Which means that I need to find the area of the 5 triangles in the shaded region and add them up. I know the area, angles and dimensions for the first green triangle and I know the areas for the remaining 4 green & white triangles but I don't know how to make sense of the sides

Answer 1

Notice that the area of the larger triangle is equal to thrice the area you need to find plus the area of the equilateral triangle at the centre. Find the side of the smaller one, plug the value in the formula, a couple of transpositions and ta-da!

Answer 2

Compute the area of the second-largest triangle, by subtracting three of the triangles you found. You now get a ratio between the area of the largest and second largest triangle; this ratio must also be the ratio between the second and third largest, and etc. You can find the area of the smallest triangle this way. Note that the large triangle is composed of the smallest triangle, and three copies of the shaded region, so you can simply subtract the area of the smallest from the largest, and divide by three.