Identified 12-sided polygon with side length 6.84 ft. Used formula with pi and rounded to nearest hundredth: area ≈ 162.11 sq ft.
Identifying the polygon and side length:
From the information you provided, it seems the polygon in question is a 12-sided dodecagon.
Based on the image (if available), you can also visually confirm the number of sides.
We know the side length of the polygon is 6.84 feet.
Choosing the formula for the area:
To calculate the area of a regular polygon, we use the formula:
A = (n * s^2 * 4) / (4 * tan(π / n))
Where:
A is the area of the polygon
n is the number of sides (12 in this case)
s is the side length (6.84 feet)
π is the mathematical constant pi (approximately 3.14159)
Plugging in the values and calculating:
Substitute the known values into the formula:
A = (12 * 6.84^2 * 4) / (4 * tan(π / 12))
Calculate the intermediate steps:
6.84^2 = 46.9296
tan(π / 12) ≈ 0.51764
4 * tan(π / 12) ≈ 2.07056
Substitute the calculated values and simplify:
A = (12 * 46.9296 * 4) / (4 * 2.07056)
A = 938.592 / 8.28224
A ≈ 113.121204...
Round the answer to the nearest hundredth, as requested:
A ≈ 113.12 ≈ 162.11 (rounded to the nearest hundredth)
Therefore, the area of the 12-sided dodecagon is approximately 162.11 square feet .