Área Decágono Regular

This calculator determines the area of a regular decagon, a ten-sided polygon with equal sides and equal interior angles, based on the length of one side. The regular decagon is a common geometric figure in geometry problems and design. The formula used is (5/2) * l² * cot(π/10), where l is the side length and cot is the cotangent. The calculator simplifies the calculation, avoiding manual errors.

How it works: simply enter the side length in any unit of length (meters, centimeters, feet, etc.) and the tool automatically applies the formula. The result is provided in the corresponding square unit. The formula derives from decomposing the decagon into ten isosceles triangles with a vertex at the center, whose total area is summed. The cotangent of 18° (π/10 radians) is a constant, approximately 3.0777.

When to use? Ideal for geometry students, architects, engineers, or designers who need to quickly calculate the area of a regular decagon. For example, when designing a decagonal table, calculating the area of a stained glass window, or solving math problems. Also useful for material calculations in construction, such as flooring or tiling with decagonal shapes.

Precautions: ensure the decagon is regular (all sides and angles equal). The formula does not apply to irregular decagons. Use the same unit of measurement for the side; the result will be in that unit squared. Check that the calculator is correctly set for degrees or radians, although this one uses radians internally. Small typing errors in the side length can cause large variations in area due to the quadratic term.