The dartboard shown at right 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:

1. The dart hits the center triangle?

   Hint (a):

   How many smaller triangles make up the bigger triangle?

   Answer (a):

   The probability is $\frac{1}{4}$.

2. The dart misses the center triangle but hits the board?

   Hint (b):

   How many smaller triangles can be hit if the center one is missed?