To find the volume,we would first need to find the height of square pyramid, by it's base edge and slant height using Pythagoras theorem:
![{height }^(2) = {13}^(2) - {10}^(2) \\ {height }^(2) = 69 \\ height = √(69)](https://img.qammunity.org/2019/formulas/mathematics/high-school/bawrcnl730wbcfyrirl2cvyyt7k6uwpzca.png)
We can then use the pyramid formula to find the volume:
![base \: * \: height \: * (1)/(3)](https://img.qammunity.org/2019/formulas/mathematics/high-school/w3jxtzavex2tlg35xgac837zy8durqg0xv.png)
In this case,the volume will be:
10×_/69×1/3
=27.68874...
≈27.7 units^3
Hope it helps!