To determine the total surface area of a triangular prism, we need to calculate the areas of its triangular faces and rectangular faces based on the measurements provided:
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Area of each triangular face: We can calculate the area of the triangular face using the formula for the area of a triangle:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
Given:
- Base = 5 cm
- Height = 4 cm
\[ \text{Area of the triangular face} = \frac{1}{2} \times 5 , \text{cm} \times 4 , \text{cm} = \frac{1}{2} \times 20 , \text{cm}^2 = 10 , \text{cm}^2 \]
Since the prism has two triangular faces, the total area of the triangular faces is: \[ 2 \times 10 , \text{cm}^2 = 20 , \text{cm}^2 \]
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Area of the rectangular faces: The prism has three rectangular faces. We can calculate the area of each rectangular face using the formula:
\[ \text{Area} = \text{length} \times \text{width} \]
Assuming:
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The smallest rectangular face has a height of 3 cm (this face corresponds to the edge of 3 cm of the triangle)
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The middle rectangular face corresponds to the edge of 4 cm
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The largest rectangular face corresponds to the edge of 5 cm
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Smallest rectangular face (height 3 cm, base 5 cm): \[ \text{Area} = 5 , \text{cm} \times 3 , \text{cm} = 15 , \text{cm}^2 \]
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Middle rectangular face (height 4 cm, base 5 cm): \[ \text{Area} = 5 , \text{cm} \times 4 , \text{cm} = 20 , \text{cm}^2 \]
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Largest rectangular face (height 4 cm, base 11 cm): \[ \text{Area} = 11 , \text{cm} \times 4 , \text{cm} = 44 , \text{cm}^2 \]
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Total Surface Area of the Triangular Prism: Now, we can add the areas of the triangular faces and the rectangular faces together:
- Total area of triangular faces = 20 cm²
- Area of the smallest rectangular face = 15 cm²
- Area of the middle rectangular face = 20 cm²
- Area of the largest rectangular face = 44 cm²
\[ \text{Total Surface Area} = 20 , \text{cm}^2 + 15 , \text{cm}^2 + 20 , \text{cm}^2 + 44 , \text{cm}^2 = 99 , \text{cm}^2 \]
Thus, the final answers are:
- Area of each triangular face = 10 cm²
- Area of the smallest rectangular face = 15 cm²
- Area of the middle rectangular face = 20 cm²
- Area of the largest rectangular face = 44 cm²
- TOTAL Surface Area of the Triangular Prism = 99 cm²