To calculate the lateral surface area of a triangular prism, you can follow these steps:
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Identify the dimensions: You need the height of the prism and the lengths of the sides of the triangular base. Let's denote the lengths of the sides of the triangular base as \(a\), \(b\), and \(c\), and the height of the prism as \(h\).
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Calculate the perimeter of the triangular base: The perimeter \(P\) of the triangular base is given by: \[ P = a + b + c \]
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Calculate the lateral surface area: The lateral surface area \(A_L\) of the prism is given by the formula: \[ A_L = P \times h \] Here, \(h\) is the height of the prism.
Putting it all together, the formula for the lateral surface area of a triangular prism can be summarized as: \[ A_L = (a + b + c) \times h \]
Example:
Suppose you have a triangular prism with sides of the base measuring \(3\) cm, \(4\) cm, and \(5\) cm, and a height of \(10\) cm.
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Calculate the perimeter of the triangular base: \[ P = 3 + 4 + 5 = 12 , \text{cm} \]
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Calculate the lateral surface area: \[ A_L = 12 , \text{cm} \times 10 , \text{cm} = 120 , \text{cm}^2 \]
So the lateral surface area of the triangular prism is \(120 , \text{cm}^2\).
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