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A triangular prism whose base is a scalene triangle that measures 9 in, 11in, and 13 in respectively and with a height of 8in. The height of the prism is 19in.

User Rifthy
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Final answer:

To calculate the volume of a triangular prism, first determine the area of the scalene triangle base using Heron's formula, and then multiply by the prism's height.

Step-by-step explanation:

The student has asked about the volume of a triangular prism with a scalene triangle base. First, we need to calculate the base area. Since the triangle is scalene, Heron's formula will be used, which requires the semi-perimeter (s) that is half the sum of the triangle's sides. For the given sides of 9 in, 11 in, and 13 in, the semi-perimeter is s = (9 + 11 + 13) / 2 = 16.5 in. Heron's formula for the area (A) is A = √(s(s-a)(s-b)(s-c)), which when calculated gives the area of the triangle. To find the volume of the prism (V = Ah), we multiply the base area (A) by the height of the prism (19 in).

User Amgohan
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