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?