Given:
Base: 5 in, 4 in., 3 in.
Height: 8 in.
Use Heron's formula, which allows us to compute the area based on the side lengths to find the base area of the triangular base:
Area = √[s(s - a)(s - b)(s - c)]
Where:
a, b, and c = the triangle side lengths
s = the semi-perimeter of the triangle, calculated as (a + b + c) / 2.
The semi-perimeter:
s = (5 + 4 + 3) / 2
s = 12 / 2
s = 6
Calculate the base area using Heron's formula:
Area = √[6(6 - 5)(6 - 4)(6 - 3)]
= √[6(1)(2)(3)]
= √[36]
= 6 in²
Volume = Base Area × Height
= 6 in² × 8 in
= 48 in³
Therefore, the volume of the prism is 48 cubic inches.