Railway embankment

The railway embankment section is an isosceles trapezoid, and the bases' sizes are in the ratio of 5:3. The arms have a length of 5 m, and the embankment height is 4.8 m. Calculate the size of the embankment section area.

Final Answer:

S =  26.88 m²

Step-by-step explanation:

$$\begin{gathered} 3a=5c \\ r=5\text{m} \\ h=4.8\text{m} \\ x=\sqrt{r^2-h^2}=\sqrt{5^2-4.8^2}=\frac{7}{5}=1.4\text{m} \\ 3\cdot a=5\cdot c \\ a=c+2\cdot x \\ a=c+2\cdot 1.4 \\ 3a-5c=0 \\ a-c=2.8 \\ Row2-\frac{1}{3}\cdot Row1\to Row2 \\ 0.67c=2.8 \\ c=\frac{2.8}{0.66666667}=4.2 \\ a=\frac{0+5c}{3}=\frac{0+5\cdot 4.2}{3}=7 \\ a=7 \\ c=\frac{21}{5}=4.2 \\ S=h\cdot \frac{a+c}{2}=4.8\cdot \frac{7+4.2}{2}=26.88{\text{m}}^2 \end{gathered}$$

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