Question

I completely lost!! SOMEONE PLEASE HELP!

Answer 1

To determine the area of the shaded region, you must
1: find the area of the whole rectangle
2: find the area of the non-shaded rectangle inside
3: subtract the non-shaded rectangle from the whole rectangle. 

Answer 2

This is easier than you think.

The area of a rectangle is l x w, right?
Well, you have two rectangles: The rectangle that is the whole of the picture, and the tiny rectangle inside the shaded area.
So the big rectangle:

A = 10 x 14 5/8
    = 146.25
The insdie rectangle:
A = 5 x 2 1/2
   = 12.5

Now take the small one away from the large one:
146.25 - 12.5 = 133.75
Or, to put it in the same way as the question:
133 3/4 inches²