Un prisma recto con base cuadrada de lado 3u y de altura 6u tiene como área total

1. Break Down the Problem

To find the total surface area of a rectangular prism with a square base, we need to consider:

• The area of the base.
• The area of the four lateral faces.
• The dimensions given: side length $a = 3u$ and height $h = 6u$.

2. Relevant Concepts

• Area of one square base: $A_{base} = a^2$.
• Area of one lateral face (rectangle): $A_{lateral} = a \times h$.
• Total surface area of the prism: $A_{total} = 2 \times A_{base} + 4 \times A_{lateral}$

3. Analysis and Detail

1. Calculate the Area of the Base: $A_{base} = a^2 = (3u)^2 = 9u^2$
2. Calculate the Area of One Lateral Face: $A_{lateral} = a \times h = 3u \times 6u = 18u^2$
3. Calculate the Total Surface Area:
   • Base areas: $2 \times A_{base} = 2 \times 9u^2 = 18u^2$
   • Lateral areas: $4 \times A_{lateral} = 4 \times 18u^2 = 72u^2$
   • Combine both areas: $A_{total} = 18u^2 + 72u^2 = 90u^2$

4. Verify and Summarize

We calculated the areas of the bases and lateral faces separately and summed them up correctly. The calculations were verified step by step.

Final Answer

The total surface area of the prism is $90u^2$.