Children pool

The bottom of the children's pool is a regular hexagon with a = 60 cm side. The distance of opposing sides is 104 cm, the height of the pool is 45 cm.
A) How many liters of water can fit into the pool?
B) The pool is made of a double layer of plastic film. How many m² of foil do you need to make one pool?

Correct answer:

V =  421.2 l
S =  5.112 m²

Step-by-step explanation:

$$\begin{gathered} a=60\mathrm{/}10=6\text{ dm } \\ x=104\mathrm{/}10={\displaystyle \frac{52}{5}}=10.4\text{ dm } \\ h=45\mathrm{/}10={\displaystyle \frac{9}{2}}=4.5\text{ dm } \\ v=x\mathrm{/}2=10.4\mathrm{/}2={\displaystyle \frac{26}{5}}=5.2 \\ {S}_1=a\cdot v\mathrm{/}2=6\cdot 5.2\mathrm{/}2={\displaystyle \frac{78}{5}}=15.6{\text{dm}}^2 \\ {S}_6=6\cdot S_1=6\cdot 15.6={\displaystyle \frac{468}{5}}=93.6{\text{dm}}^2 \\ V=S_6\cdot h=93.6\cdot 4.5={\displaystyle \frac{2106}{5}}={\displaystyle \frac{2106}{5}}\text{ l}=421.2\text{ l} \end{gathered}$$

$$\begin{gathered} o=6\cdot a=6\cdot 6=36\text{ dm } \\ S=2\cdot (S_6+o\cdot h)\mathrm{/}100=2\cdot (93.6+36\cdot 4.5)\mathrm{/}100={\displaystyle \frac{639}{125}}={\displaystyle \frac{639}{125}}{\text{m}}^2=5.112{\text{m}}^2 \end{gathered}$$

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