Answer:
471.1 square units
Explanation:
A regular nonagon is a 9-sided polygon with sides of equal length.
The apothem of a regular polygon is the distance from the center of the polygon to the midpoint of one of its sides.
Therefore, the given diagram shows a regular nonagon with an apothem of 12 units.
The side length (s) of a regular polygon can be calculated using the apothem formula:

Given values:
Substitute the given values into the formula to create an expression for the side length (s):



The standard formula for an area of a regular polygon is:

Substitute the found expression for s together with n = 9 and a = 12 into the formula and solve for A:




Therefore, the area of a regular nonagon with an apothem of 12 units is 471.1 square units, rounded to the nearest tenth.