Wooden 3

A wooden board 2.5 m long has a cross-section in the shape of a regular trapezoid whose parallel sides have lengths of 1.2 dm and 8 cm. The height of the trapezoid is 3 cm. Calculate:

a) the surface area of ​​the board to calculate the consumption of stain
b) the weight of the board if the density of the wood is 600kg/m³
c) how many boards can we load on a 3t truck?

Correct answer:

S =  6862.7756 cm²
m =  4.5 kg
n =  666

Step-by-step explanation:

$$\begin{gathered} l=2.5\text{m}\to \text{cm}=2.5\cdot 100\text{cm}=250\text{cm} \\ a=1.2\text{dm}\to \text{cm}=1.2\cdot 10\text{cm}=12\text{cm} \\ c=8\text{cm} \\ v=3\text{cm} \\ {S}_1=\frac{a+c}{2}\cdot v=\frac{12+8}{2}\cdot 3=30{\text{cm}}^2 \\ b=\sqrt{v^2+((a-c)/2{)}^2}=\sqrt{3^2+((12-8)/2{)}^2}=\sqrt{13}\text{cm}\doteq 3.6056\text{cm} \\ o=a+b+c+b=12+3.6056+8+3.6056\doteq 27.2111\text{cm} \\ S=2\cdot S_1+o\cdot l=2\cdot 30+27.2111\cdot 250=6862.7756{\text{cm}}^2 \end{gathered}$$

$$\begin{gathered} m_1=3\text{t}\to \text{kg}=3\cdot 1000\text{kg}=3000\text{kg} \\ n=\lfloor m_1/m\rfloor =\lfloor 3000/4.5\rfloor =666 \end{gathered}$$

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