Answer:
80.4 square units (nearest tenth)
Explanation:
The given diagram shows a regular dodecagon (12-sided polygon) with an apothem of 5 units.
The apothem of a regular polygon is the distance from the center of the polygon to the midpoint of one of its sides.
We can calculate the side length of a regular polygon given its apothem using the following formula:

Substitute n = 12 and a = 5 into the equation to create an expression for s:


Now we can use the standard formula for an area of a regular polygon:

Substitute the found expression for s, n = 12 and a = 5 into the formula and solve for A:





Therefore, the area of a regular dodecagon with an apothem of 5 units is 80.4 square units, rounded to the nearest tenth.