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what is the total surface of the rectangle

To find the total surface area of the rectangular prism, we need to calculate the area of all six faces. Each rectangular prism has three pairs of opposite faces with equal areas.

The dimensions given are:
- Length \( l = 12 \) cm
- Width \( w = 6 \) cm
- Height \( h = 3 \) cm

The formula for the surface area \( S \) of a rectangular prism is:
\[
S = 2lw + 2lh + 2wh
\]

Let's calculate each term:
1. \( 2lw = 2 \times 12 \times 6 = 144 \) cm²
2. \( 2lh = 2 \times 12 \times 3 = 72 \) cm²
3. \( 2wh = 2 \times 6 \times 3 = 36 \) cm²

Adding them together:
\[
S = 144 + 72 + 36 = 252 \, \text{cm}^2
\]

Thus, the total surface area of the rectangular prism is **252 cm²**.

Would you like further clarification on the steps?

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1. How would the surface area change if the height was doubled?
2. What is the surface area formula for a cube?
3. How does surface area relate to volume for a rectangular prism?
4. What are real-life applications of calculating surface areas?
5. How would you find the surface area if only given diagonal dimensions?

**Tip:** Remember to calculate each pair of faces separately when dealing with surface areas of prisms.

What is the total surface area of the rectangular prism in square centimeters?

Learn how to find the total surface area of a rectangular prism with dimensions 12 cm, 6 cm, and 3 cm. This step-by-step guide covers the surface area formula and provides a detailed solution for a geometry problem suitable for Grades 6-8.

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