Two square pyramids with base 4 cm and slant height 5 cm are joined at their base so that they share a common base. The surface area of the resulting geometric shape is the sum of their individual surfaces from which the surface area of the base has to be eliminated.
A pyramid has a surface area given by `A = B + P*L/2` where B is the area of the base, P is the perimeter of the base and L is the slant height.
For the resulting shape, the area is `A = 2*P*L/2` .
Substituting the given values of the dimensions of the pyramids, we have `A = 2*4*4*5/2`
=> `A = 4*4*5`
=> `A = 16*5`
=> `A = 80`
The surface area of the resulting geometrical shape is 80 cm^2.