As shown in the figure, the cross section of a reservoir dam is an isosceles trapezoid with a crest width of 6 meters and a dam height of 10 meters. The slope of slope AB is 1:2 (AR: BR). Now, if the crest width and slope gradient are unchanged, how much earthwork is needed to reinforce a 50 meter long dam

As shown in the figure, the cross section of a reservoir dam is an isosceles trapezoid with a crest width of 6 meters and a dam height of 10 meters. The slope of slope AB is 1:2 (AR: BR). Now, if the crest width and slope gradient are unchanged, how much earthwork is needed to reinforce a 50 meter long dam

∵ in RT △ ABR, the slope of slope AB is 1:2, ar = 10, ∵ br = 20m, ∵ trapezoid ABCD is isosceles trapezoid, then BC = 2Br + ad = 46m, ∵ s trapezoid ABCD = (AD + BC) × ar △ 2 = 260m2, ∵ the slope of AB has no change before and after the transformation, and eh ⊥ BC is made at point h through point E. according to the title meaning, eh = 10 + 2 = 12M, ∵ pH = 2eh = 24m, the bottom length of trapezoid after the transformation is 2 × 24 + 6 = 54m The area of trapezoid is (54 + 6) × 12 △ 2 = 360 square meters. After the transformation, the extra area is s trapezoid epcf-s trapezoid ABCD = 360-260 = 100 square meters, so the required earthwork is 100 × 50 = 5000 cubic meters. A: 5000 cubic meters