To find the height of the square-based pyramid, we can use the formulas for both the volume and the area of the pyramid.
- The volume \( V \) of a square-based pyramid is given by the formula: \[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \] Given the volume \( V = 250 \) cubic yards and the area of the base \( A = 50 \) square yards, we can use the formula to find the height \( h \).
First, we can rearrange the volume formula to solve for height \( h \): \[ h = \frac{3V}{\text{Base Area}} \]
Substituting the known values: \[ h = \frac{3 \times 250}{50} \] \[ h = \frac{750}{50} \] \[ h = 15 \text{ yards} \]
Thus, the height of the pyramid is 15 yards.