Prism surface calculation

Calculate the surface of a prism with a square base whose mantle is a rectangle with sides of 18 cm and 8 cm. How many solutions does the task have? List all solutions.

Final Answer:

S₁ =  184.5 cm²
S₂ =  152 cm²

Step-by-step explanation:

$$\begin{gathered} x=18\text{cm} \\ c=8\text{cm} \\ x=o=4a \\ a=x/4=18/4=\frac{9}{2}=4.5\text{cm} \\ {S}_1=2\cdot a^2+x\cdot c=2\cdot 4.5^2+18\cdot 8=184.5{\text{cm}}^2 \end{gathered}$$

$$\begin{gathered} x=8\text{cm} \\ c=18\text{cm} \\ a=x/4=8/4=2\text{cm} \\ {S}_2=2\cdot a^2+x\cdot c=2\cdot 2^2+8\cdot 18=152{\text{cm}}^2 \end{gathered}$$

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