Final answer:
The program needs to calculate the handling fee and shipping charge for art figures based on the volume of the shape and total processing charges.
Step-by-step explanation:
To calculate the handling fee and shipping charge for the art figures, the artist will need to determine the volume of each shape. The volume of a tetrahedron can be found using the formula V = (sqrt(2)/12) * a³, where a is the length of one side. The volume of an octahedron can be found using the formula V = (sqrt(2)/3) * a³, where a is the length of one side. The volume of a dodecahedron can be found using the formula V = (15 + 7sqrt(5))/4 * a³, where a is the length of one side.
Once the volumes are calculated, the artist can determine the handling fee and shipping charge based on the total processing charges. The specific calculations for these charges would need to be provided or determined based on the artist's pricing structure.
Overall, the program needs to calculate the volume of each shape using the given formulas and use those volumes to calculate the handling fee and shipping charge based on the total processing charges.