The Missing Block

### I found this problem in a puzzle book titled "The Ultimate
Clever Puzzle Book". I was so intrigued by this that I decided
to investigate what underlies the mystery and recruited Matt and
BJ to help me figure it out.

### The problem goes as such:

### Start with an 8 unit by 8 unit square

###

### Count the number of blocks that make up this pattern to find
the the area; the area of this square is 64 units

### Now, cut along the two black lines and the one blue line in
the picture below

###

### You have two congruent triangles and two congruent trapezoids

### The objective now is to rearrange these four pieces into a
rectangle, which should look line the one below

###

### Now, how many blocks are there?

### The new figure is thirteen blocks long and five blocks high
which gives us sixty five blocks. Where did the extra block come
from?

###