Final answer:
To calculate the area of a regular polygon with an exterior angle of 18° and a side of 16 cm, first determine the polygon is a 20-sided figure, then find the apothem, and finally calculate the area, which is approximately 0.76 m².
Step-by-step explanation:
To determine the area of a regular polygon with exterior angles of 18° and sides measuring 16 cm, we need to use the property that the sum of exterior angles of any polygon is 360°. Thus, the number of sides n is calculated as 360° divided by the exterior angle, or n = 360° / 18° = 20. Now that we know the polygon is a 20-sided polygon, we can calculate its perimeter by multiplying the length of one side by the number of sides, which is perimeter = 16 cm × 20 = 320 cm. The apothem a of the polygon can be calculated using the formula a = s / (2 × tan(π / n)), where s is the side length. In this case, a = 16 cm / (2 × tan(π/20)) ≈ 47.61 cm. The area A of the polygon is given by A = (1/2) × perimeter × apothem or A = (1/2) × 320 cm × 47.61 cm ≈ 7615.20 cm² or 0.76152 m² when converted to square meters, rounded to two decimal places as 0.76 m².