Trapezoidal 43931

How many trees are planted in a trapezoidal park with bases of 35.7m, 13.3m, arms of 20m and 22m, and a height of 19 m if one tree needs nine m²?

Correct answer:

n =  51

Step-by-step explanation:

$$\begin{gathered} a=35.7\text{m} \\ c=13.3\text{m} \\ b=20\text{m} \\ d=22\text{m} \\ v=19\text{m} \\ {S}_1=9{\text{m}}^2 \\ S=\frac{a+c}{2}\cdot v=\frac{35.7+13.3}{2}\cdot 19=\frac{931}{2}=465\frac{1}{2}=465.5{\text{m}}^2 \\ {n}_1=S/S_1=\frac{931}{2}/9=\frac{931}{2\cdot 9}=\frac{931}{18}=51\frac{13}{18}\doteq 51.7222 \\ n=\lfloor n_1\rfloor =\lfloor 51.7222\rfloor =51 \end{gathered}$$

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