Embankment

The perpendicular cross-section of the embankment around the lake has the shape of an isosceles trapezoid. Calculate the perpendicular cross-section, where the bank is 4 m high, the upper width is 7 m, and the legs are 10 m long.

Correct answer:

S =  64.6606 m²

Step-by-step explanation:

$$\begin{gathered} h=4\text{m} \\ c=7\text{m} \\ r=10\text{m} \\ x=\sqrt{r^2-h^2}=\sqrt{10^2-4^2}=2\sqrt{21}\text{m}\doteq 9.1652\text{m} \\ a=c+2\cdot x=7+2\cdot 9.1652\doteq 25.3303\text{m} \\ S=(a+c)\cdot h/2=(25.3303+7)\cdot 4/2=64.6606{\text{m}}^2 \end{gathered}$$

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