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?

Result

S =  163.8 m²

Solution:

$h=2 \ \text{m} \ \\ a=10 \ \text{m} \ \\ c=18 \ \text{m} \ \\ b=7 \ \text{m} \ \\ d=b=7 \ \text{m} \ \\ h_{ 2 }=5.7 \ \text{m} \ \\ \ \\ S_{ 1 }=(a+c) \cdot \ h_{ 2 }/2=(10+18) \cdot \ 5.7/2=\dfrac{ 399 }{ 5 }=79.8 \ \text{m}^2 \ \\ o=a+b+c+d=10+7+18+7=42 \ \text{m} \ \\ \ \\ S_{ 2 }=h \cdot \ o=2 \cdot \ 42=84 \ \text{m}^2 \ \\ S=S_{ 1 }+S_{ 2 }=79.8+84=\dfrac{ 819 }{ 5 }=163.8 \ \text{m}^2$

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