Un prisma recto con base cuadrada de lado 3u y de altura 6u tiene como área totalGrupo de opciones de respuesta501009040

1. Break Down the Problem

We need to calculate the total surface area of a right rectangular prism (also known as a cuboid) that has a square base. Given:

• Side length of the base (a) = 3u
• Height (h) = 6u

2. Relevant Concepts

The total surface area (A) of a prism can be calculated using the formula:

$A = 2A_{base} + A_{lateral}$

Where:

• $A_{base} = a^2$ (area of the base)
• $A_{lateral} = perimeter_{base} \cdot height$

The perimeter of the base (square base) is given by:

$P_{base} = 4a$

3. Analysis and Detail

1. Calculate the area of the base: $A_{base} = a^2 = (3u)^2 = 9u^2$

2. Calculate the lateral surface area: $P_{base} = 4a = 4 \cdot 3u = 12u$ $A_{lateral} = P_{base} \cdot h = 12u \cdot 6u = 72u^2$

3. Now calculate the total surface area: $A = 2A_{base} + A_{lateral} = 2 \cdot 9u^2 + 72u^2 = 18u^2 + 72u^2 = 90u^2$

4. Verify and Summarize

After performing the calculations:

• $A_{base} = 9u^2$
• $A_{lateral} = 72u^2$
• Therefore, the total area $A = 90u^2$.

Final Answer

The total surface area of the prism is 90.