the angle on triangular prism is 6 in, 12 in, 4 in, and 5 in

Question

Determine the volume of the triangular prism.
A. 120 in^3
B. 144 in^3
C. 240 in^3
D. 288 in^3
E. 1440 in^3

Answer 1

B. 144 in^3

To find the volume of a triangular prism, you first need to calculate the area of the triangular base and then multiply it by the height of the prism.

The formula for the area of a triangle is A = 1/2 * base * height. In this case, the base and height of the triangle are 6 in and 4 in respectively, so the area of the triangular base is 1/2 * 6 * 4 = 12 in^2.

Then, you multiply the area of the triangular base by the height of the prism, which is 5 in: 12 in^2 * 5 in = 60 in^3.

Since a prism is essentially two congruent triangles placed back to back, the volume of the prism is calculated by finding the total volume of both triangles, so you multiply the volume of one triangle by 2: 60 in^3 * 2 = 120 in^3.

Therefore, the correct answer is B. 144 in^3.