The surface area is the area of all the surfaces. Let's find the area of the square and the four triangles and add them together:
Square:
[tex]\sf A=s^2[/tex]
[tex]\sf A=10^2[/tex]
[tex]\sf A=100~in^2[/tex]
Triangles 1, 2, 3, & 4:
[tex]\sf A=\dfrac{1}{2}bh[/tex]
[tex]\sf A=\dfrac{1}{2}(10)(12)[/tex]
[tex]\sf A=60~in^2[/tex]
Now add them all up:
[tex]\sf 100+60+60+60+60=\boxed{\sf 340~in^2}[/tex]
So the surface area of the square pyramid is 340 square inches.
