1. the picture shows a feeding trough that is shaped like a right prism. (a) surface a and b are identical trapezoids. what are the lengths of the bases of the trapezoids? what is the height? (b) surfaces a and b will be painted blue. what is the total area that will be painted blue? (c) the edges of the trapezoids need to be sanded. a piece of sandpaper advertises that it can sand up to 80 cm. will one piece of sandpaper be enough to sand the edges of one trapezoid? explain.

A) as shown in the diagram, in the trapezoid larger side length is 35 cm and shorter side length is 19 cm.

b) next we are asked to calculate the areas of the trapezoids to paint the area blue. 
Area of trapezoid =1/2* (length of shorter side + longer side )*height
height of trapezoid = 15 cm 
Area = 1/2 * (19 + 35) * 15
        = 1/2* 54 *15
        = 405 cm²
As both surfaces A and B need to be painted, we need to multiply the area of one trapezoid by 2
total area = 405 * 2 = 810 cm²

c)
edges of the trapezoids needs to be sanded. Therefore we need to calculate the lengths of all the edges. 
this means that we need to add up all the edges of both the trapezoids.
perimeter of trapezoid A = 19 + 35 + 17 + 17 
                                      = 88 cm
perimeter of trapezoid B = 88 cm
one sandpaper can sand only 80 cm, but the total edge length is 88 cm therefore one sandpaper is not enough.