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To calculate the surface area of the triangular prism, we need to compute the areas of all its faces. A triangular prism has five faces: two triangular bases and three rectangular lateral faces.

### Step-by-Step Breakdown:

1. **Area of the triangular base**:
   - The base of the triangle is 27 mm, and its height is 14 mm.
   - The area of a triangle is given by:
     \[
     A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 27 \times 14
     \]

2. **Lateral faces (rectangles)**:
   - The three rectangular faces are:
     1. One rectangle with dimensions 21 mm (length) and 27 mm (width).
     2. One rectangle with dimensions 9 mm (length) and 27 mm (width).
     3. One rectangle with dimensions 18 mm (length) and 27 mm (width).

3. **Total Surface Area**:
   - The surface area \( S \) of the prism is the sum of the areas of the two triangular bases and the three rectangular faces:
     \[
     S = 2 \times A_{\text{triangle}} + A_{\text{rect1}} + A_{\text{rect2}} + A_{\text{rect3}}
     \]

I'll calculate this now.The total surface area of the triangular prism is \( 1674 \, \text{mm}^2 \).

Would you like any further details or have questions?

Here are five related questions:
1. How do you calculate the volume of this triangular prism?
2. What are the properties of a triangular prism in geometry?
3. Can the surface area formula change if the prism is oblique?
4. How would the surface area change if the dimensions of the triangle were different?
5. How does the surface area affect the material used to construct a physical model of this prism?

**Tip**: Always ensure that all dimensions are in the same unit when calculating areas and volumes to avoid errors.

Calculate the surface area of the triangular prism. Dimensions are: 18 mm, 14 mm, 27 mm (triangular base) and 21 mm, 9 mm, 18 mm for the rectangular sides.

Learn how to calculate the surface area of a triangular prism with a base of 18 mm, 14 mm, and 27 mm, and rectangular sides of 21 mm, 9 mm, and 18 mm. This guide covers key geometric concepts, including surface area formulas for triangular prisms. Suitable for students in Grades 8-10.

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