



 
Donnie, The volume is the area of the crosssection times te width of 115 feet. The shape of the crosssection is a trapezoid, a figure bounded by 4 lines, two of which are parallel. The area of a trapezoid is the average of the lengths of the parallel sides times the distance between the parallel sides. You have parallel sides of length 4 and 18 inches but you don't know the distance between them. It should be close to 176' but lets find it more exactly. Before I begin I am going to change all the dimensions to yards since you asked for the volume in cubic yards. In yards the dimensions arre 176/3 = 58.67, 115/3 = 38.33, 18/36 = 0.50 and 4/36 = 0.11. To find the distance between the parallel sides d I am going to use Pythagoras theorem. Triangle ABC is a right triangle BC = 58.67 yards, CA = 0.5  0.11 = 0.39 yards and AB = d yards. Thus
and hence
Thus two 2 decimal places d and BC are the same length. The area of the trapezoidal crosssection is thus
Finally the volume of fill you need is 17.89 × 38.33 = 686 cubic yards. Harley  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 