Answer:
400 ft³
Step-by-step explanation:
The volume of a square pyramid can be calculated as:

Where a is the side of the square and h is the height of the pyramid.
Now, we need to calculate the height using the slant height, so we will use the following equation:
![h=\sqrt[]{s^2-(a^2)/(4)}](https://img.qammunity.org/2023/formulas/mathematics/college/r53qgdbe2yvd02ew6z5h1n781awixi0sde.png)
So, the height of the pyramid is equal to:
![\begin{gathered} h=\sqrt[]{13^2-(10^2)/(4)} \\ h=\sqrt[]{169-(100)/(4)} \\ h=\sqrt[]{169-25} \\ h=\sqrt[]{144} \\ h=12 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/2z1pvg7xotseo673q5j3kx6yjy4giesrhq.png)
Then, the volume of the square pyramid is equal to:

Therefore, the answer is 400 ft³