https://file.aiquickdraw.com/mathbot/file/1729277734696ajcghfd8.jpg

What is the surface area of this rectangular prism, in square meters?

To find the surface area of the rectangular prism shown in the image, we use the formula for the surface area of a rectangular prism:

\[
\text{Surface Area} = 2lw + 2lh + 2wh
\]
where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.

From the image, the dimensions are:
- \( l = 13 \, \text{m} \),
- \( w = 7 \, \text{m} \),
- \( h = 3 \, \text{m} \).

Now, let's calculate each term:
\[
2lw = 2(13)(7) = 182 \, \text{m}^2
\]
\[
2lh = 2(13)(3) = 78 \, \text{m}^2
\]
\[
2wh = 2(7)(3) = 42 \, \text{m}^2
\]

Adding them together:
\[
\text{Surface Area} = 182 + 78 + 42 = 302 \, \text{m}^2
\]

Thus, the surface area of the rectangular prism is **302 square meters**.

Would you like a detailed explanation or have any questions?

Here are 5 related questions you might find interesting:
1. How do you calculate the volume of this rectangular prism?
2. What would the surface area be if the height were doubled?
3. If the width was decreased by 2 meters, how would the surface area change?
4. How does the surface area formula change for a cube?
5. How would you calculate the diagonal of the rectangular prism?

**Tip**: When calculating the surface area of 3D shapes, always ensure you are considering all six faces (or surfaces) properly.

Learn how to calculate the surface area of a rectangular prism with dimensions 13m, 7m, and 3m. This step-by-step guide explains the key formula for calculating the surface area of rectangular prisms and is suitable for students in Grades 5-8.

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