Determine the volume of the triangular prism.
4in, 5in, 6in, 12in
The volume of a triangular prism is calculated as V = (1/2) * base area * height, where the base of the prism is a triangle.
First, calculate the area of the base triangle:
Base = 4in + 5in + 6in = 15in
Using Heron's formula, where s is the semi-perimeter of the triangle, it can be calculated as:
s = (4in + 5in + 6in) / 2 = 7.5in
Area = sqrt[7.5in * (7.5in - 4in) * (7.5in - 5in) * (7.5in - 6in)] = sqrt(7.5 * 3.5 * 2.5 * 1.5) = sqrt(91.875) = 9.58in^2
Now, calculate the volume:
V = (1/2) * 9.58in^2 * 12in = 57.5in^3
Therefore, the volume of the triangular prism is 57.5 cubic inches.