If h = 6 units, X = 9 units, Y = 13 units, and Z = 17 units, then what is the volume of the triangular prism shown above?

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To find the volume of a triangular prism, you need the height and the base area of the triangular base. In this case, the height (h) is given as 6 units. However, the base area is not provided in the question. To find it, we can use the formula for the area of a triangle: (base × height) / 2.

Given the lengths of the sides of the triangular base (X = 9 units, Y = 13 units, and Z = 17 units), you can calculate the semi-perimeter (s) using the formula: s = (X + Y + Z) / 2.

s = (9 + 13 + 17) / 2 = 39 / 2 = 19.5

Now, we can use Heron's formula to find the area (A) of the triangle. Heron's formula states that the area of a triangle with sides of length X, Y, and Z and semi-perimeter s is:

A = sqrt(s × (s - X) × (s - Y) × (s - Z))

Plugging in the given lengths, we have:

A = sqrt(19.5 × (19.5 - 9) × (19.5 - 13) × (19.5 - 17))
A = sqrt(19.5 × 10.5 × 6.5 × 2.5)
A ≈ sqrt(1992.75)
A ≈ 44.64

Now that we have the base area (A) and the height (h), we can calculate the volume (V) of the triangular prism using the formula: V = A × h.

V ≈ 44.64 × 6
V ≈ 267.84

Therefore, the volume of the triangular prism is approximately 267.84 cubic units.