https://file.aiquickdraw.com/mathbot/file/1727800863752xupu0xbw.jpg

The solid in the image appears to be a triangular prism. To find both the surface area and the volume of this prism, we need to follow specific formulas based on the dimensions provided.

### 1. **Surface Area of the Triangular Prism**:
The surface area \( A \) of a triangular prism can be calculated using the following formula:

\[
A = 2 \times \text{Base Area} + \text{Lateral Area}
\]

- The base of the prism is a triangle, and its area can be calculated as:

\[
\text{Base Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
  where base = 3.2 cm and height = 2.4 cm.

\[
\text{Base Area} = \frac{1}{2} \times 3.2 \times 2.4 = 3.84 \, \text{cm}^2
\]

- The lateral area is the sum of the areas of the three rectangular faces. Each rectangular face has a width equal to the height (or slant) of the prism and a length equal to one of the triangle's sides:
  - First side: \( 3.2 \, \text{cm} \)
  - Second side: \( 2.0 \, \text{cm} \)
  - Third side: \( 4.0 \, \text{cm} \)
  
  So, the lateral area is:
  
\[
\text{Lateral Area} = (3.2 \times 4) + (2.0 \times 4) + (4.0 \times 4) = 12.8 + 8 + 16 = 36.8 \, \text{cm}^2
\]



Find the surface area and volume of the triangular prism. The dimensions are 4.0 cm, 2.4 cm, 2.0 cm, and 3.2 cm.

Calculate the surface area and volume of a triangular prism with dimensions 4.0 cm, 2.4 cm, 2.0 cm, and 3.2 cm. This detailed guide covers the formulas for surface area and volume for students in Grades 6-8.

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