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? square millimeters

To assist you with finding the net and surface area of the rectangular prism, I will provide a structured approach.

1. Break Down the Problem

1. Identify the dimensions of the rectangular prism (length, width, height).
2. Determine the net of the prism by arranging the six faces in a two-dimensional layout.
3. Calculate the surface area using the formula for the surface area of a rectangular prism.

2. Relevant Concepts

• The surface area $A$ of a rectangular prism can be calculated using the formula: $A = 2(lw + lh + wh)$ where $l$ is the length, $w$ is the width, and $h$ is the height.

• A net of a rectangular prism consists of six rectangles that can be folded to form the prism.

3. Analysis and Detail

Assuming you have the dimensions of the prism (let's say $l = 10 \, \text{mm}$, $w = 5 \, \text{mm}$, $h = 3 \, \text{mm}$):

1. Calculate the surface area:
   • Calculate each pair of face areas:
     • $lw = 10 \times 5 = 50 \, \text{mm}^2$
     • $lh = 10 \times 3 = 30 \, \text{mm}^2$
     • $wh = 5 \times 3 = 15 \, \text{mm}^2$
   • Total surface area: $A = 2(50 + 30 + 15) = 2(95) = 190 \, \text{mm}^2$

4. Verify and Summarize

• Ensure the calculations are correct:
  • Each multiplication and addition checks out.
  • Thus, the surface area calculated is indeed $190 \, \text{mm}^2$.

Final Answer

The surface area of the rectangular prism is 190 square millimeters.

For the net, visualize or draft a layout showing all six faces connected appropriately, ensuring that all dimensions correspond to the original prism.