Trapezoid floor slats

The room has a trapezoidal floor plan; we need to polish it. The parallel sides in a trapezoid are 4,800 mm and 4,400 mm long, and the oblique sides are 4,600 mm and 5,100 mm long. There are two 900 mm wide doors in the room. One strip measures 250 cm and costs CZK 150. How many slats will we need?

Final Answer:

n =  7
p =  1050 Kc

Step-by-step explanation:

$$\begin{gathered} a=4800\text{mm}\to \text{m}=4800:1000\text{m}=4.8\text{m} \\ c=4400\text{mm}\to \text{m}=4400:1000\text{m}=4.4\text{m} \\ b=4600\text{mm}\to \text{m}=4600:1000\text{m}=4.6\text{m} \\ d=5100\text{mm}\to \text{m}=5100:1000\text{m}=5.1\text{m} \\ x=900\text{mm}\to \text{m}=900:1000\text{m}=0.9\text{m} \\ l=250\text{cm}\to \text{m}=250:100\text{m}=2.5\text{m} \\ o=a+b+c+d-2\cdot x=4.8+4.6+4.4+5.1-2\cdot 0.9=\frac{171}{10}=17\frac{1}{10}=17.1\text{m} \\ {n}_0=o/l=17.1/2.5=\frac{171}{25}=6\frac{21}{25}=6.84 \\ n=\lceil n_0\rceil =\lceil 6.84\rceil =7 \end{gathered}$$

$p=150\cdot n=150\cdot 7=1050\text{Kc}$

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