A straight horizontal road is to be constructed through rough terrain. The width of the road is to be 10 m, with the sides of the embankment sloping at 1 (vertical) in 2 (horizontal), as shown in Figure 2.7. Obtain a formula for the cross-sectional area of the road and its embankment, taken at right angles to the road, where the rough ground lies at a depth x below the level of the proposed road. Use your formula to complete the table below, and draw a graph to represent this function.

What is the value given by the formula when x = –2, and what is the meaning of that value?

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x/m Areal m 2h Figure 2.7 Th 0 0 1 10 m 2 28 xm 3 4 5 100