Surface Area of Rectangular Prisms Quick Check

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Question
Use the image to answer the question.

An illustration shows a two-dimensional net of a rectangular prism composed of 6 rectangles.



The net of a rectangular prism is shown. What is the surface area of the rectangular prism?

Answer 1

To find the surface area of a rectangular prism, you'll need the dimensions of the prism's length (l), width (w), and height (h). Since we are dealing with a net, you can identify these dimensions by observing the individual rectangles that make up the net.

Here’s the step-by-step method to calculate the surface area:

1. Identify the dimensions (length, width, and height) from the net:
- Typically, you will observe three sets of rectangles: each set representing pairs of identical faces of the prism.

2. Calculate the area of each pair:
- The rectangular prism has three different sets of faces.
- Each pair of faces has the following areas:
- Front and back faces: \( l \times h \)
- Left and right faces: \( w \times h \)
- Top and bottom faces: \( l \times w \)

3. Multiply each area by 2 (as each pair consists of two rectangles):
- \( 2 \times (l \times h) \)
- \( 2 \times (w \times h) \)
- \( 2 \times (l \times w) \)

4. Sum up all these areas to get the total surface area:
- \( \text{Surface Area} = 2(l \times h) + 2(w \times h) + 2(l \times w) \)
- Simplified: \( \text{Surface Area} = 2(lh + wh + lw) \)

If you provide the specific dimensions of the prism (length, width, and height), I can give you the exact surface area. Without those dimensions, the surface area formula is as follows:
\[ \text{Surface Area} = 2(lh + wh + lw) \]