To determine the total surface area of a triangular prism, we need to calculate the areas of the triangular faces and the rectangular faces. Let's break this down step by step using the dimensions provided.
1. Area of the Triangular Face
If we assume the triangle is defined by the dimensions provided (for example, using 30.5 cm and 28.4 cm as the base and height):
Using the formula for the area of a triangle: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \] Assuming base = 30.5 cm and height = 28.4 cm: \[ \text{Area of one triangular face} = \frac{1}{2} \times 30.5 \times 28.4 = \frac{1}{2} \times 864.2 \approx 432.1 , \text{cm}^2 \]
2. Area of the Rectangular Faces
For the rectangular faces, we will use the following dimensions:
- Smallest rectangular face: width 5.1 cm and height (the length of the prism, you may want to confirm this value).
- Middle rectangular face (you may assign dimensions accordingly).
- Largest rectangular face (same as above, please confirm the dimension).
If we proceed with the assumption that the height of the prism is 5.1 cm:
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Smallest rectangular face (base = 30.5 cm): \[ \text{Area} = \text{base} \times \text{height} = 30.5 \times 5.1 = 155.55 , \text{cm}^2 \]
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Middle rectangular face (base = 28.4 cm): \[ \text{Area} = 28.4 \times 5.1 = 145.84 , \text{cm}^2 \]
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Largest rectangular face (using the length, you may assign dimensions accordingly; assume base = 27.9 cm): \[ \text{Area} = 27.9 \times 5.1 = 142.29 , \text{cm}^2 \]
3. Total Surface Area Calculation
To find the total surface area, sum all the calculated areas together: \[ \text{Total Surface Area} = 2 \times \text{Area of triangular face} + \text{Area of smallest face} + \text{Area of middle face} + \text{Area of largest face} \] Assuming the above calculations for areas: \[ \text{Total Surface Area} = 2 \times 432.1 + 155.55 + 145.84 + 142.29 \] \[ = 864.2 + 155.55 + 145.84 + 142.29 = 1307.88 , \text{cm}^2 \]
Final Answers:
- Area of ONE triangular face = 432.1 cm²
- Area of the smallest rectangular face = 155.55 cm²
- Area of the middle rectangular face = 145.84 cm²
- Area of the largest rectangular face = 142.29 cm²
- TOTAL Surface Area of the Triangular Prism = 1307.88 cm²
Please feel free to adjust any of the values according to your specific measurements.