https://file.aiquickdraw.com/mathbot/file/172670636788597r7qpz1.jpg

The given image shows a triangular prism. To find the surface area and volume, we need to use the following formulas:

### 1. Surface Area of the Triangular Prism:
The surface area (SA) is calculated by adding the areas of the two triangular bases and the three rectangular sides.

1. **Area of the triangular base:**
   - The triangle has a base of \(3.2 \, \text{cm}\) and a height of \(2.4 \, \text{cm}\).
   - Area of the triangle = \(\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 3.2 \times 2.4\).

2. **Areas of the three rectangles:**
   - **Rectangle 1:** \(3.2 \, \text{cm} \times 4.0 \, \text{cm}\).
   - **Rectangle 2:** \(4.0 \, \text{cm} \times 2.0 \, \text{cm}\).
   - **Rectangle 3:** \(2.0 \, \text{cm} \times 3.2 \, \text{cm}\).

3. **Total Surface Area:**
   - SA = \(2 \times\) (area of the triangle) + (areas of the three rectangles).

### 2. Volume of the Triangular Prism:
The volume (V) is found by multiplying the area of the triangular base by the prism's length (4.0 cm).

- Volume = (area of the triangular base) \(\times\) prism length.

Let's calculate these values:The calculations give us the following results:

- **Surface Area:** \( 36.5 \, \text{cm}^2 \) (rounded to the nearest tenth)
- **Volume:** \( 15.4 \, \text{cm}^3 \) (rounded to the nearest tenth)

Would you like more details on the calculations, or do you have any questions?

Here are some related questions to consider:

1. How do you find the surface area of different types of prisms?
2. What are the key differences between calculating the volume of prisms and pyramids?
3. How do changes in dimensions affect the surface area and volume of a solid?
4. Can you explain how the surface area and volume formulas are derived for prisms?
5. What are real-world applications of finding the surface area and volume of prisms?

**Tip:** Always double-check units when working with area and volume to ensure consistency!

Find the surface area and volume of the solid triangular prism. Dimensions: base of the triangle = 3.2 cm, height of the triangle = 2.4 cm, and length of the prism = 4.0 cm. Other side lengths: 2.0 cm.

Learn how to calculate the surface area and volume of a triangular prism with a 3.2 cm base and 2.4 cm height. The prism has a length of 4.0 cm and triangular side lengths of 2.0 cm. Detailed steps are provided for finding both the surface area and volume.

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