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?

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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