Cross-section 23491

The cross-section of the railway embankment is an isosceles trapezoid, the bases of which are in a ratio of 5:3. The arms have a 5 m embankment height v = 4.8 m. Calculate the section area S.

Correct answer:

S =  26.88 m²

Step-by-step explanation:

$$\begin{gathered} r=5\text{m} \\ v=4.8\text{m} \\ a:c=5:3 \\ S=(a+c)v/2 \\ {a}_1^2=r^2-v^2 \\ {a}_1=\sqrt{r^2-v^2}=\sqrt{5^2-4.8^2}=\frac{7}{5}=1.4\text{m} \\ a=c+2a_1 \\ a/c=5/3 \\ (c+2a_1)c=5/3 \\ 3c+6a_1=5c \\ 6a_1=2c \\ c=3\cdot a_1=3\cdot \frac{7}{5}=\frac{3\cdot 7}{5}=\frac{21}{5}=4.2\text{m} \\ a=c+2\cdot a_1=\frac{21}{5}+2\cdot \frac{7}{5}=7\text{m} \\ S=\frac{a+c}{2}\cdot v=\frac{7+4.2}{2}\cdot 4.8=\frac{672}{25}{\text{m}}^2=26.88{\text{m}}^2 \end{gathered}$$

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