To determine the total surface area of the triangular prism, we need to calculate the area of the triangular faces and the areas of the rectangular faces, then sum them up to find the total surface area.
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Find Area of Each Triangular Face: The area of a triangle can be calculated using the formula: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \] Suppose the base is \(b\) cm and the height is \(h\) cm. Thus, the area for one triangular face is: \[ \text{Area of triangular face} = \frac{1}{2} \times b \times h \] Since there are two triangular faces, then: \[ \text{Total area of triangular faces} = 2 \times \text{Area of one triangular face} \]
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Find Areas of the Rectangular Faces:
Let’s label the sides of the triangular prism:- Smallest rectangular face: This face uses the smallest side of the triangle as one of its dimensions. Suppose its length is \(l_1\) cm and its width (short side of triangle) is \(s_1\) cm, then: \[ \text{Area of smallest rectangular face} = \text{length} \times \text{width} = l_1 \times s_1 \]
- Middle rectangular face: Using the middle side of the triangle, where the length is \(l_2\) cm and width is the next dimension \(s_2\) cm: \[ \text{Area of middle rectangular face} = l_2 \times s_2 \]
- Largest rectangular face: Using the largest side of the triangle, where the length is \(l_3\) cm and width is the largest dimension \(s_3\) cm: \[ \text{Area of largest rectangular face} = l_3 \times s_3 \]
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Total Surface Area: The total surface area of the triangular prism can be calculated as: \[ \text{Total Surface Area} = (\text{Area of triangular faces}) + (\text{Area of smallest rectangular face}) + (\text{Area of middle rectangular face}) + (\text{Area of largest rectangular face}) \]
Once you provide the specific dimensions for the base and height of the triangular faces (as well as the dimensions of the rectangular faces), I can help you calculate each area and the total surface area of the prism.