Tin sheet

How much sheet metal is needed for a box in the shape of a triangular prism with a base edge of 20 cm, base height of 15 cm, and prism height of 30 cm? An additional 10% of sheet metal is needed for joins.

Final Answer:

S =  2310 cm²

Step-by-step explanation:

$$\begin{gathered} a=20\text{cm} \\ h=30\text{cm} \\ {h}_2=15\text{cm} \\ r=100\%+10\%=1+\frac{10}{100}=1.1 \\ {S}_1=\frac{a\cdot h_2}{2}=\frac{20\cdot 15}{2}=150{\text{cm}}^2 \\ o=3\cdot a=3\cdot 20=60\text{cm} \\ {S}_2=o\cdot h=60\cdot 30=1800{\text{cm}}^2 \\ {S}_3=2\cdot S_1+S_2=2\cdot 150+1800=2100{\text{cm}}^2 \\ S=r\cdot S_3=1.1\cdot 2100=2310{\text{cm}}^2 \end{gathered}$$

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