Final answer:
The area of a regular nonagon with a radius of 6 units is calculated using the formula ½ × n × r^2 × sin(360°/n), and is approximately 104.1 square units, when rounded to two significant figures.
Step-by-step explanation:
The question asks to find the area of a regular nonagon with a radius of 6 units. To find the area of a regular polygon, you can use the formula:
A = \( \frac{1}{2}\) × n × r^2 × sin(\( \frac{360}{n}\)°)
Where:
- A is the area of the polygon,
- n is the number of sides (9 for a nonagon),
- r is the radius of the polygon (6 units in this question),
- and sin is the sine function of the angle in degrees.
The angle in a regular nonagon is \( \frac{360°}{9}\) = 40°. So, the area would be calculated as:
A = \( \frac{1}{2}\) × 9 × 6^2 × sin(40°) = 9 × 18 × sin(40°) ≈ 9 × 18 × 0.6428 ≈ 1041.97,
but since we are looking for the area in two significant figures, the answer is 104 (in calculator display it may show as 104.1 due to rounding).
Thus, the area of the regular nonagon with a radius of 6 units is approximately 104.1 square units.