What is the surface area of the sides and closed rectangular end? ____ sq. ft.

Without the roof panels, the surface area (except for the open panel) is 176.25 sq. ft.
With the roof panels, the surface area (except for the open panel) is 196.67 sq. ft. 

The area of the rectangular sections (the sides without gables) is given by 10*6 = 60 sq. ft.  There are two of these sides, for a total of 2*60 = 120 sq. ft.

The gables are triangles, which have an area formula of
A = 1/2bh

For the gables, this is 1/2(1.5)(7.5) = 5.625 sq. ft.  Since there are two of them, this makes 2*5.625 = 11.25 sq. ft.

The closed side under a gable has an area of 6*7.5 = 45 sq. ft.

The two roof panels have an area of (4 1/12)(2 1/2) each:
49/12(5/2) = 245/24

There are two of them, which makes 490/24 = 20.42 sq. ft.

Without the roof panels, we have 45+11.25+120 = 176.25 sq. ft.
With the roof panels, we have 45+11.25+120+20.42 = 196.67 sq. ft.