The third-graders are painting shoeboxes in our class. if it takes dominic one minute to paint 4 in.², how long will it take them to paint the outside of this box?

The dimensions of the exterior of the (closed) shoebox are 6 by 7 by 4 inches.  First find the surface area of the shoebox.  To do this, you must find the surface area of one top, of one end and of one side.  Then multiply all of these calculations by 2.

Total surface area = ?

Now divide the total surface area by (4 square inches per minute), to determine how many minutes it will take the kid to paint the whole exterior of the shoebox.

The largest angle is opposite the side that measures 17.
We know all 3 sides so we will use the Law of Cosines
cosine (C) = (a^2 + b^2 -c^2) / 2ab
cosine (C) = ( 10^2 + 13^2 -17^2) / 2 * 10 * 13
cosine (C) = (100 + 169 -289) / 260
cosine (C) = -20 / 260
cosine (C) = -.0769230769
arc cosine (-.0769230769 ) = 94.412 Degrees

Source:
http://www.1728.org/trigtut2.htm