The volume of a square pyramid is
[tex]V=\frac{1}{3}\cdot a^2\cdot h[/tex]Where a is the length of each base side.
First, we have to find a using the perimeter.
[tex]\begin{gathered} P=4a \\ 56in=4a \\ a=\frac{56in}{4} \\ a=14in \end{gathered}[/tex]Then, we find h using Pythagorean's Theorem,
[tex]c^2=a^2+b^2[/tex]Where c = 25in, b = 7in, and a represents the height h
[tex]\begin{gathered} (25in)^2=h^2+(7in)^2 \\ 625in^2=h^2+49in^2 \\ h^2=625in^2-49in^2 \\ h=\sqrt[]{576in^2} \\ h=24in \end{gathered}[/tex]Now, we find the volume
[tex]\begin{gathered} V=\frac{1}{3}\cdot(14in)^2\cdot24in \\ V=\frac{1}{3}\cdot196in^2\cdot24in \\ V=1,568in^3 \end{gathered}[/tex]