The area of the irregular polygon is square units.

To find the area of this shape youd have to break it up. If you broke it into the left section and the right bottom section youd get 2 rectangles and the area of a rectangle is defined as A=Length*Width. The left would be a 3*4 rectangle making its area 12 units^2 and the right would have a height of (3-2) units and a length of (7-4) units making its area 1*3 or just 3 units^2, if you add both areas you get the total area, which is 15 units^2

Break it up into chunks: the small rectangle and the big rectangle.
subtract 7 and 4 to get the big side of the rectangle, and subtract 3 and 2 to get the small side. then find the area of the big rectangle and small rectangle to get the area of the entire rectangle. area equals 15 units^2

The shelves will hold 270 books in total