Cross-section 79984

A ditch with a cross-section in the shape of an isosceles trapezoid with bases of 3 m and 5 m and arms of length 2 m is 2.5 meters deep and 10 meters long. How many cubic meters of soil did they have to excavate when digging it?

Correct answer:

V =  100 m³

Step-by-step explanation:

$$\begin{gathered} a=3\text{m} \\ c=5\text{m} \\ b=2\text{m} \\ h=2.5\text{m} \\ L=10\text{m} \\ {S}_1=\frac{a+c}{2}\cdot h=\frac{3+5}{2}\cdot 2.5=10{\text{m}}^2 \\ V=S_1\cdot L=10\cdot 10=100{\text{m}}^3 \end{gathered}$$

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