All you need to check is to multiply the answer by 3, and add the area of the circle. Hopefully that will add up to the area of the entire triangle
Yeah, I created this in the morning and the answer was over 12 instead of yours, so I thought I had messed up at the beginning and got super frustrated I was second guessing myself a lot when I was trying to find the height of the triangle, since I wasn't allow to use my iPad at the time. I realized I should've cut the triangle in half to use the 30-60-90 theorem..
(I'm having a friend of mine do the problem at the same time as you, so if they're both the same, most likely the answer will be right)
Also, I'll attach an image:
I'm gonna find the empty space of the triangle not taken up my the circles to create a mathematical constant. There's probably a function or summation used to find it, though