Pool whitewashing

The pool is in the shape of a vertical prism with a bottom in the shape of an isosceles trapezoid with dimensions of the bases of the trapezoid 10 m and 18 m, and arms 7 m are 2 m deep. During spring cleaning, the bottom and walls of the pool must be whitewashed. How much m² needs to be whitewashed?

Final Answer:

S =  164.4239 m²

Step-by-step explanation:

$$\begin{gathered} a=10 \\ c=18 \\ r=7 \\ h=2 \\ o=a+c+2\cdot r=10+18+2\cdot 7=42 \\ {S}_1=o\cdot h=42\cdot 2=84 \\ {h}_1=\sqrt{r^2-((a-c)/2{)}^2}=\sqrt{7^2-((10-18)/2{)}^2}=\sqrt{33}\doteq 5.7446 \\ {S}_2=(a+c)\cdot h_1/2=(10+18)\cdot 5.7446/2=14\sqrt{33}\doteq 80.4239 \\ S=S_1+S_2=84+80.4239=164.4239{\text{m}}^2 \end{gathered}$$

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