Decagon Area
Calculate the area of any regular decagon instantly using the formula A = (5/2) x a^2 x sqrt(5 + 2sqrt5). Free online decagon area calculator for students, teachers, and geometry professionals.
About This Calculator
Use this free online decagon area calculator to compute the area of any regular decagon. Enter the side length and instantly get the area using the formula A = (5/2) x a^2 x sqrt(5 + 2sqrt5). This decagon area tool is perfect for geometry homework, architectural design, tiling projects, and any application involving 10-sided polygons.
Frequently Asked Questions
What is the formula for the area of a regular decagon?
The area of a regular decagon with side length a is A = (5/2) x a^2 x sqrt(5 + 2sqrt5). This formula is derived by dividing the decagon into 10 congruent isosceles triangles, each with base a and height equal to the apothem.
How do you find the area of an irregular decagon?
For an irregular decagon, divide it into triangles, rectangles, or other known shapes, calculate each area separately, then sum them. Alternatively, use the shoelace formula if you have the coordinates of all 10 vertices.
What is the apothem of a regular decagon?
The apothem (or inradius) of a regular decagon is the distance from the center to the midpoint of any side. It equals a / (2 x tan(18 deg)), where a is the side length. The apothem is used in the alternative area formula: A = (1/2) x perimeter x apothem.
How do you calculate decagon area from the circumradius?
Given the circumradius R, the area of a regular decagon is A = (5/2) x R^2 x sin(36 deg). Alternatively, A = (5R^2/2) x sqrt((5 - sqrt5)/2). Both formulas give the same result.
What is the sum of interior angles of a decagon?
The sum of all interior angles of any decagon is 1440 degrees. This is calculated using the formula (n - 2) x 180 deg where n = 10, giving (10 - 2) x 180 = 1440 degrees. For a regular decagon, each angle is 144 degrees.
Can this calculator handle different units?
Yes, the decagon area calculator accepts any unit of measurement for the side length. The area result is displayed in the corresponding square units (e.g., cm^2, m^2, in^2, ft^2). Simply enter your side length in your preferred unit.
Is the decagon area calculator free?
Yes, all calculators on Calculy including the decagon area calculator are completely free to use with no registration, download, or hidden fees.