Answer: To calculate the height of the triangular prism, we'll first need to find the area of the rectangular surfaces. The formula for the volume (V) of a triangular prism is given by:
V = (1/2) * base * height * length,
where:
base = base of the triangular base (in this case, it's the side with length 9 cm),
height = height of the triangular base (we need to find this),
length = length of the prism (in this case, it's the side with length 17 cm).
We are given that the volume of the prism is 864 cm³, so we can write the equation as:
864 = (1/2) * 9 * height * 17.
Now, let's solve for the height:
864 = (1/2) * 9 * height * 17
864 = 76.5 * height
Divide both sides by 76.5:
height = 864 / 76.5
height = 11.294 cm (approximately).
The height of the triangular prism is approximately 11.294 cm.