To find the surface area of the rectangular prism using the net provided, we'll need the dimensions of all the rectangles in the net and sum up the areas of these individual rectangles.
Based on your description, let's list out the dimensions:
- Two small rectangles: \( 2 \text{ ft} \times 5 \text{ ft} \)
- Two large rectangles: \( 5 \text{ ft} \times 8 \text{ ft} \)
- Two mid-sized rectangles (assumed to be the same as the ends):
Let's calculate the areas for each set of rectangles:
1. **Small Rectangles:**
\[
\text{Area of one small rectangle} = 2 \text{ ft} \times 5 \text{ ft} = 10 \text{ square feet}
\]
\[
\text{Total area for two small rectangles} = 10 \text{ square feet} \times 2 = 20 \text{ square feet}
\]
2. **Large Rectangles:**
\[
\text{Area of one large rectangle} = 5 \text{ ft} \times 8 \text{ ft} = 40 \text{ square feet}
\]
\[
\text{Total area for two large rectangles} = 40 \text{ square feet} \times 2 = 80 \text{ square feet}
\]
3. **Mid-sized Rectangles:** (Assuming dimensions from description)
\[
\text{Area of one mid-sized rectangle} = 2 \text{ ft} \times 8 \text{ ft} = 16 \text{ square feet}
\]
\[
\text{Total area for two mid-sized rectangles} = 16 \text{ square feet} \times 2 = 32 \text{ square feet}
\]
Finally, add the areas of all rectangles together to get the surface area of the rectangular prism:
\[
\text{Total Surface Area} = 20 \text{ square feet} + 80 \text{ square feet} + 32 \text{ square feet} = 132 \text{ square feet}
\]
Thus, the surface area of the rectangular prism is \(132\) square feet.
Surface Area of Rectangular Prisms Quick Check
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Question
Use the image to answer the question.
An illustration shows the unfolded version of a rectangular prism composed of 6 rectangles. There are four adjoining rectangles positioned horizontally. The first and third are similar and smaller. The top of the first rectangle is labeled 2 feet. The second and fourth are similar and bigger. The fourth rectangle is labeled 8 feet on the right side. The second rectangle shares the top and bottom sides with two similar rectangles, one on each side. The top rectangle is labeled as 5 feet on the top side.
Use this net to find the surface area of the rectangular prism it represents.
1 answer