If h = 8 units, X = 9 units, Y = 6 units, and Z = 21 units, what is the volume of the triangular prism shown above?
To find the volume of a triangular prism, you multiply the area of the base triangle by the height of the prism.
The base triangle has sides X, Y, and Z. Using Heron's formula, we can calculate the area of the base triangle:
s = (X + Y + Z) / 2 = (9 + 6 + 21) / 2 = 18 units
Area = √[s(s-X)(s-Y)(s-Z)]
= √[18(18-9)(18-6)(18-21)]
= √[18(9)(12)(-3)]
= √5832
≈ 76.36 units
Since the height of the prism is 8 units, the volume of the triangular prism is:
Volume = Base Area * Height
= 76.36 * 8
≈ 610.88 units
Therefore, the volume of the triangular prism shown above is approximately 610.88 cubic units.