The approximate area of a regular 12-sided polygon, or dodecagon, with each side measuring 1 inch, can be calculated using the formula for the area of a regular polygon, yielding roughly 11.1962 square inches using the formula (1/4)×12×1²×cot(π/12).
To calculate the area of a 12-sided polygon, also known as a dodecagon, with each side measuring 1 inch, one method is to break the polygon into 12 congruent isosceles triangles with two equal sides of 1 inch.
However, since the height of these triangles is not readily available without trigonometric functions, an alternative approximate method would be to use the formula for the area of a regular polygon:
Area = (1/4)n×s²×cot(π/n), where n is the number of sides and s is the length of each side.
In this case:
Area = (1/4) * 12 * 1² * cot(π/12) ≈ 11.1962 square inches.
The exact area will require use of a calculator with trigonometric function capabilities to compute the cotangent of π/12.