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).