Look at the picture.
Use the Pythagorean theorem:
[tex]\left(\dfrac{1}{2}b\right)^2+12^2=13^2\\\\\dfrac{1}{4}b^2+144=169\ \ \ |-144\\\\\dfrac{1}{4}b^2=25\ \ \ |\cdot4\\\\b^2=100\to b=\sqrt{100}\to b=10\ cm[/tex]
The area of the triangle:
[tex]A_t=\dfrac{10\cdot12}{2}=60\ cm^2[/tex]
The area of the square:
[tex]A_s=10^2=100\ cm^2[/tex]
The surface area of rectangular square pyramid:
[tex]SA=4A_t+A_s\\\\SA=4\cdot60+100=340\ cm^2[/tex]
