Cross sections reduced to end areas and an earthwork volume

Given

• Two cross sections taken 100.00 ft apart on a roadway in cut, at stations 12+00 and 13+00. All dimensions in feet.
• Subgrade template: level, 24.00 ft wide, extending 12.00 ft either side of centerline. Backslopes are 1.5 horizontal to 1 vertical.
• Cross-section notes at 12+00, given as cut above subgrade at offset from centerline (negative left, positive right): left slope stake 6.2 at -21.3; left subgrade edge 3.4 at -12.0; centerline 2.6 at 0.0; right subgrade edge 4.1 at +12.0; right slope stake 7.0 at +22.5.
• Cross-section notes at 13+00: left slope stake 4.4 at -18.6; left subgrade edge 2.0 at -12.0; centerline 1.5 at 0.0; right subgrade edge 3.2 at +12.0; right slope stake 5.6 at +20.4.
• Areas are carried to 0.1 square foot and volumes to the nearest cubic yard.

Required

• Verification that the slope stakes are consistent with a 1.5 to 1 backslope.
• The end area of each cross section.
• The volume of excavation between the two sections by average end area, in cubic yards.

Work it through yourself before reading on - the solution below shows every step, so there is no way to skim it without giving the answer away.