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31 March, 06:55

The surface area of a triangular prism is 34 square inches. What is the surface area of a similar prism with dimensions that are 3 times as great as the original prism?

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  1. 31 March, 07:13
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    306 square inches

    Step-by-step explanation:

    The surface are of a triangular prism is given as:

    A = ab + 3bh

    where a = Length of side

    b = base length

    h = height of the prism

    If the dimensions are 3 times as great, that means a becomes 3a, b becomes 3b and h = 3h

    Therefore, the new surface area becomes:

    A1 = (3a * 3b) + 3 (3b * 3h) = 9ab + 27bh

    A1 = 9 (ab + 3bh)

    => A1 = 9A

    The surface area of the initial prism is 34 square inches, therefore, the surface area of the new prism will be:

    A1 = 9 * 34 = 306 square inches
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