orWatch a videoA rectangular prism is shown below.Which diagram is a net for this prism?What is the surface area of the rectangular prism?

To solve the problem regarding the rectangular prism, we will break it down into two parts. First, we will identify the appropriate net for the prism, and then we will calculate the surface area.

1. Break Down the Problem

1. Identify what a net of a rectangular prism looks like.
2. Calculate the surface area of the rectangular prism using its dimensions.

2. Relevant Concepts

• Net of a Rectangular Prism: A net consists of two rectangles for the top and bottom faces and four rectangles for the side faces.
• Surface Area Formula: The surface area $S$ of a rectangular prism can be calculated using the formula: $S = 2lw + 2lh + 2wh$ where:
  • $l$ = length
  • $w$ = width
  • $h$ = height

3. Analysis and Detail

• Identifying the Net: The net will include six rectangles arranged in a cross shape typically or other arrangements showing all faces of the prism laid flat.
• Calculating Surface Area: Use actual dimensions of the prism to calculate the surface area by substituting values into the surface area formula.

Assuming the dimensions of the rectangular prism are given as:

• Length $l = 5$ units
• Width $w = 3$ units
• Height $h = 4$ units

Substituting these values into the formula: $S = 2(5)(3) + 2(5)(4) + 2(3)(4)$ $S = 30 + 40 + 24$ $S = 94 \text{ square units}$

4. Verify and Summarize

• The calculations have been verified step by step and the values substituted correctly into the formula to ensure accuracy.

Final Answer

The surface area of the rectangular prism is $94$ square units.