The formula for the volume \( V \) of a triangular pyramid (or any pyramid) is given by:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
In this case, the base area \( A \) is given as 13 square feet and the volume \( V \) is 52 cubic feet. We can plug these values into the formula to solve for the height \( h \).
\[ 52 = \frac{1}{3} \times 13 \times h \]
To isolate \( h \), we first multiply both sides by 3:
\[ 156 = 13 \times h \]
Next, divide both sides by 13:
\[ h = \frac{156}{13} = 12 \]
Thus, the height of Fatima’s pyramid is 12 ft.