https://file.aiquickdraw.com/mathbot/file/1729872005990w5z2tmy2.jpg

The image you provided shows the net of a rectangular box with labeled dimensions. We can calculate the total surface area by finding the area of all the individual faces of the net.

From the image, the dimensions are as follows:
- The length of the box is \( 12 \, \text{cm} \).
- The height of the box is \( 7 \, \text{cm} \).
- The width of the box is \( 4.6 \, \text{cm} \).

For a rectangular prism, the surface area (total area) is calculated as the sum of the areas of all six faces.

- There are **2 large rectangular faces** with dimensions \( 12 \, \text{cm} \times 7 \, \text{cm} \).
  - Area of one face = \( 12 \times 7 = 84 \, \text{cm}^2 \).
  - Total for two faces = \( 2 \times 84 = 168 \, \text{cm}^2 \).

- There are **2 smaller rectangular faces** with dimensions \( 7 \, \text{cm} \times 4.6 \, \text{cm} \).
  - Area of one face = \( 7 \times 4.6 = 32.2 \, \text{cm}^2 \).
  - Total for two faces = \( 2 \times 32.2 = 64.4 \, \text{cm}^2 \).

- There are **2 other rectangular faces** with dimensions \( 12 \, \text{cm} \times 4.6 \, \text{cm} \).
  - Area of one face = \( 12 \times 4.6 = 55.2 \, \text{cm}^2 \).
  - Total for two faces = \( 2 \times 55.2 = 110.4 \, \text{cm}^2 \).

Now, summing all these areas:

\[
\text{Total Surface Area} = 168 \, \text{cm}^2 + 64.4 \, \text{cm}^2 + 110.4 \, \text{cm}^2 = 342.8 \, \text{cm}^2
\]

Thus, the total surface area of the rectangular box is **342.8 cm²**.

Would you like more details or have any other questions?

Here are some related questions to explore:
1. How would the surface area change if the width was increased by 2 cm?
2. What would be the surface area of a cube with the same volume as this box?
3. How does surface area relate to volume in three-dimensional shapes?
4. Can you calculate the surface area of a cylinder with the same height as this box but a radius of 3 cm?
5. What are the differences in surface area calculations between regular prisms and pyramids?

**Tip:** Always double-check units to ensure they are consistent throughout your calculations!

Calculate the total surface area of the rectangular box based on the provided net dimensions.

Learn how to calculate the total surface area of a rectangular box with dimensions 12 cm by 7 cm by 4.6 cm. This geometry problem walks through the detailed steps to find the surface area, making it suitable for students in Grades 7-10.

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