The dartboard shown below is in the shape of an equilateral triangle. It has a smaller equilateral triangle in the center, which was made by joining the midpoints of the three edges. If a dart hits the board at random, what is the probability that:
The dart hits the center triangle?
How many smaller triangles make up the bigger triangle?
The dart misses the center triangle?
How many smaller triangles can be hit if the center one is missed?