To solve for the height of the pyramid, we need to use the formula for the volume of a pyramid, which is V = (1/3)Bh, where V is the volume, B is the area of the base, and h is the height. We are given that the volume is 51 cubic centimeters and the area of the base is 17 square centimeters, so we can substitute these values into the formula and solve for h.
51 = (1/3)(17)(h)
To solve for h, we can first simplify the right side of the equation:
51 = (17h)/3
Then, we can multiply both sides of the equation by 3 to isolate h:
153 = 17h
Finally, we can divide both sides of the equation by 17 to solve for h:
h = 9
Therefore, the height of the pyramid is 9 centimeters.