Trapezoid plot fence

The plot of land for constructing family houses is shaped like a rectangular trapezoid with bases of 21 m and 11.2 m. For CZK 2,500 per square meter, the value of the land is calculated at CZK 1,352,400. What would be the length of wire mesh needed to fence this property?

Final Answer:

x =  100.8 m

Step-by-step explanation:

$$\begin{gathered} a=21\text{m} \\ c=11.2\text{m} \\ S=1352400/2500=\frac{13524}{25}=540.96{\text{m}}^2 \\ S=\frac{a+c}{2}\cdot v \\ v=\frac{2\cdot S}{a+c}=\frac{2\cdot 540.96}{21+11.2}=\frac{168}{5}=33.6\text{m} \\ b=\sqrt{v^2+(a-c{)}^2}=\sqrt{33.6^2+(21-11.2{)}^2}=35\text{m} \\ d=v=33.6=\frac{168}{5}=33.6\text{m} \\ x=a+b+c+d=21+35+11.2+33.6=100.8\text{m} \end{gathered}$$

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