https://file.aiquickdraw.com/mathbot/file/1729579356172ybfg7rwy.jpg

To calculate the total surface area of the rectangular prism in the image, we use the following formula:

\[
\text{Surface Area} = 2lw + 2lh + 2wh
\]

Where:
- \( l = 5 \, \text{mm} \) (length)
- \( w = 2 \, \text{mm} \) (width)
- \( h = 7 \, \text{mm} \) (height)

Now, we calculate each part:

1. \( 2lw = 2(5)(2) = 20 \, \text{mm}^2 \)
2. \( 2lh = 2(5)(7) = 70 \, \text{mm}^2 \)
3. \( 2wh = 2(2)(7) = 28 \, \text{mm}^2 \)

Adding these together:

\[
\text{Total Surface Area} = 20 + 70 + 28 = 118 \, \text{mm}^2
\]

So, the total surface area of the rectangular prism is **118 mm²**.

Would you like further details or clarifications?

Here are 5 related questions:
1. How do you calculate the volume of the same prism?
2. How would the surface area change if one dimension was doubled?
3. What is the relationship between surface area and volume in rectangular prisms?
4. How can we minimize the surface area for a fixed volume in rectangular prisms?
5. How does surface area affect the material cost in manufacturing?

**Tip:** For any 3D shape, knowing the formula for surface area and volume helps in many real-world applications like packaging design and materials usage optimization.

What is the total surface area of the rectangular prism shown in the image?

Learn how to calculate the total surface area of a rectangular prism with dimensions 5 mm by 2 mm by 7 mm. Using the surface area formula for prisms, this solution walks you through the detailed steps. Suitable for students in Grades 5-7.

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