To calculate the total surface area of the triangular prism, we need to break it down into its components:
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Area of the triangular faces: If we have a triangular prism, it typically has two triangular faces. To calculate the area of one triangular face, we can use the formula for the area of a triangle:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
Let's assume:
- base = \( b \) cm
- height = \( h \) cm
Then the area of one triangular face will be:
\[ \text{Area of one triangular face} = \frac{1}{2} \times b \times h \]
Therefore, the area of both triangular faces combined will be:
\[ \text{Total area of triangular faces} = 2 \times \left( \frac{1}{2} \times b \times h \right) = b \times h \]
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Area of the rectangular faces: The prism has three rectangular faces, and we can denote their dimensions as follows:
- Smallest rectangular face (has dimensions based on one side of the triangle): width = \( a \) cm (one side of the triangle), height = \( h_p \) cm (the height of the prism)
- Middle rectangular face: width = \( b \) cm (another side of the triangle), height = \( h_p \) cm
- Largest rectangular face: width = \( c \) cm (the longest side of the triangle), height = \( h_p \) cm
The areas of these rectangular faces can be calculated as:
- Area of the smallest rectangular face = \( a \times h_p \)
- Area of the middle rectangular face = \( b \times h_p \)
- Area of the largest rectangular face = \( c \times h_p \)
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Total Surface Area: The total surface area of the triangular prism is the sum of the areas of the triangular faces and the rectangular faces:
\[ \text{Total Surface Area} = (\text{Area of two triangular faces}) + (\text{Area of smallest rectangular face}) + (\text{Area of middle rectangular face}) + (\text{Area of largest rectangular face}) \]
\[ = (b \times h) + (a \times h_p) + (b \times h_p) + (c \times h_p) \]
- Here,
- \( b \) = base of the triangle,
- \( h \) = height of the triangle,
- \( a, b, c \) = lengths of the sides of the triangle,
- \( h_p \) = height (length) of the prism.
You will need the specific measurements for the base, height, and the side lengths (as well as the height of the prism) to compute the values discussed. Once you have those values, you can plug them in and calculate the surface area accordingly. Please provide those measurements if you would like to calculate the exact values.