could you please help me out a bit...

a building is 8 feet wide and 16 feet long. it has a flat roof that is 12 feet high at one corner, and 10 feet high at each of the adjacent corners. what is the volume of the building?



I drew a diagram of the building you described. (I have assumed that the 8 by 16 base is a rectangle.)

Imagine that you are on the roof at the peak P. If you walk from P to Q your altitude decreases from 12 feet to 10 feet, that it decreases by 2 feet. PS and QR are parallel and S is 2 feet lower than P so R is 2 feet lower than Q. Thus the height h at R is
10 - 2 = 8 feet.

Now subdivide the house into two regions as in the diagram below.

One region is a rectangular box 8 ft by 16 ft by 8 ft so its volume is 8 16 8 cubic ft. The second region is the attic. Can you find its volume?