We can divide the surface of the pyramid into the following shapes:
and
In order to determine the surface area, we have to add the areas of all this shapes. That is, the area of 4 triangles and a square.
The area of a triangle is given by
[tex]A_T=\frac{b\cdot h}{2}[/tex]
where b is the lenght of the base and h is the lenght of its height.
The area of a square is given by
[tex]A_S=l^2[/tex]
where l is the lenght of its side.
So, in order to determine the surface area of the pyramid, we need to get:
[tex]A_P=4\cdot\frac{b\cdot h}{2}+b^2=2\cdot b\cdot h+b^2[/tex]
since the sides of the squares are the bases of the triangles.
Using the data we have:
[tex]A_P=2\cdot12\cdot21+12^2=504+144=648[/tex]
Thus, the surface area of the pyramid is 648 square units.
