Final answer:
The mathematical operation typically involved when calculating the area of an expanding geometric shape is multiplication.
Step-by-step explanation:
When the area of an expanding geometric shape is calculated, the mathematical operation typically involved is multiplication (option C). Multiplication is used to find the product of the length and width of the shape, resulting in the total area. For example, if you have a rectangle with a length of 5 units and a width of 3 units, you would multiply these values to find the area: 5 units x 3 units = 15 square units.