Final answer:
The lateral area of the cone-shaped hat can be expressed as a function by using the formula Lateral Area = 20πr, where r is the radius of the base.
Step-by-step explanation:
The lateral area of the cone-shaped hat can be expressed as a function using the slant height and the radius of the base. Since the slant height is constant at 20 inches, we can use the formula for the lateral area of a cone, which is given by:
Lateral Area = πr × slant height
By substituting the value of the slant height (20 inches) into the formula, we get:
Lateral Area = πr × 20
Therefore, the lateral area of the cone-shaped hat can be expressed as the function Lateral Area = 20πr.