the angle of a triangular prism is 16 in, 9 in, and 8 in
The formula for volume of a TRIANGULAR PRISM is V=(area of the base) x (height of prism)
Part 1: Find the area of one TRIANGLE BASE of the prism: Area = __ in^2
Part 2: What is the height of the prism? The height connects the 2 bases. __ in
Part 3: Find the volume of the triangular prism using V=(area of the base) x (height of prism) = in^3
Part 1: To find the area of one triangular base of the prism, we can use Heron's formula since we have all three side lengths of the triangle. Let's first calculate the semi-perimeter (s) of the triangle:
s = (16 + 9 + 8) / 2 = 16.5
Now, using Heron's formula to find the area (A) of the triangle:
A = √(s * (s - 16) * (s - 9) * (s - 8))
A = √(16.5 * (16.5 - 16) * (16.5 - 9) * (16.5 - 8))
A = √(16.5 * 0.5 * 7.5 * 8.5)
A = √(16.5 * 0.5 * 63.75)
A = √(529.3125)
A ≈ 23 in^2
Part 2: The height of the prism is along the slant height of the triangle, which is the 16 in side. Therefore, the height of the prism is 16 in.
Part 3: Now that we have the area of one triangular base and the height of the prism, we can find the volume using the formula:
V = (area of the base) x (height of prism)
V = 23 in^2 x 16 in
V = 368 in^3
Therefore, the volume of the triangular prism is 368 cubic inches.