Design and build a road, the cross section of the subgrade is trapezoidal ABCD, as shown in the figure (unit: m). Set the height of the subgrade as h, and the slope angles on both sides as α and β, known as H = 2, α = 45 °, Tan β = 12, CD = 10. (1) calculate the width of AB at the base of the road; (2) how much earthwork is required to build such a subgrade 1000 m?

(1) So AB = AE + EF + BF = AE + CD + BF = 2 + 10 + 4 = 16. (2) s trapezoid ABCD = 12 (AB + CD) · H = 12 × (10 + 16) × 2 = 26. Therefore, the required earthwork is 26 × 1000 = 26000 (M3)

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