Trapezoid 36701

The field between the two parallel roads is shaped like a trapezoid with 180m and 100m long bases. The distance between the roads is 80m. When the yield of this type of cereal is 8.5 tons from 1 hectare, how many tons of barley were harvested in the field? /1ha = 10,000 m²/. How many meters of mesh are needed to fence the field?

Correct answer:

m =  9.52 t
x =  473.1371 m

Step-by-step explanation:

$$\begin{gathered} a=180\text{m} \\ c=100\text{m} \\ h=80\text{m} \\ S=\frac{a+c}{2}\cdot h=\frac{180+100}{2}\cdot 80=11200{\text{m}}^2 \\ {S}_1=S\to \text{ha}=S:10000\text{ha}=11200:10000\text{ha}=1.12\text{ha} \\ m=8.5\cdot S_1=8.5\cdot \frac{28}{25}=\frac{238}{25}\text{t}=9.52\text{t} \end{gathered}$$

$$\begin{gathered} d=h=80\text{m} \\ b=\sqrt{h^2+(a-c{)}^2}=\sqrt{80^2+(180-100{)}^2}=80\sqrt{2}\text{m}\doteq 113.1371\text{m} \\ x=a+b+c+d=180+113.1371+100+80=473.1371\text{m} \end{gathered}$$

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