Pool

The prism-shaped pool is 2 m deep with a bottom of the isosceles trapezoid with base dimensions of 10 m and 18 m and arm legs 7 m long and 5.7 m long. During the spring cleaning, the bottom and walls of the pool must be painted. How many m² of paint should be used?

Correct result:

S =  163.8 m²

Solution:

$$\begin{gathered} h=2\text{ m } \\ a=10\text{ m } \\ c=18\text{ m } \\ b=7\text{ m } \\ d=b=7=7\text{ m } \\ {h}_2=5.7\text{ m } \\ {S}_1=(a+c)\cdot h_2\mathrm{/}2=(10+18)\cdot 5.7\mathrm{/}2={\displaystyle \frac{399}{5}}=79.8{\text{m}}^2 \\ o=a+b+c+d=10+7+18+7=42\text{ m } \\ {S}_2=h\cdot o=2\cdot 42=84{\text{m}}^2 \\ S=S_1+S_2=79.8+84={\displaystyle \frac{819}{5}}={\displaystyle \frac{819}{5}}{\text{m}}^2=163.8{\text{m}}^2 \end{gathered}$$

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