Decagon
Calculate any regular decagon property instantly -- area, perimeter, side length, circumradius, and inradius. Free online geometry calculator with formula breakdown for students, teachers, and professionals.
About This Calculator
Use this free online decagon calculator to compute the area and perimeter of any regular decagon. Simply enter the side length and get instant results with the decagon area formula A = (5/2) x a^2 x sqrt(5 + 2sqrt5) and perimeter formula P = 10a. Perfect for geometry students, math teachers, architects, and design professionals working with 10-sided polygons.
Frequently Asked Questions
How many sides does a decagon have?
A decagon has 10 sides, 10 vertices, and 10 interior angles. The name comes from the Greek words 'deka' (ten) and 'gonia' (angle). Regular decagons have all sides equal and all interior angles equal at 144 degrees each.
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 and summing their areas.
What is the interior angle of a regular decagon?
Each interior angle of a regular decagon measures 144 degrees. This is calculated using the formula (n - 2) x 180 / n where n = 10, giving (10 - 2) x 180 / 10 = 144 degrees.
What is the exterior angle of a regular decagon?
Each exterior angle of a regular decagon measures 36 degrees. The sum of all exterior angles in any polygon is 360 degrees, so for a decagon each exterior angle is 360 / 10 = 36 degrees.
How do you calculate the perimeter of a decagon?
The perimeter of a regular decagon is simply 10 times the side length: P = 10a. For an irregular decagon, you sum the lengths of all 10 sides individually.
What is the circumradius of a regular decagon?
The circumradius (R) of a regular decagon with side length a is R = a / (2 x sin(pi/10)) = a / (2 x sin(18 deg)). This is the radius of the circumscribed circle that passes through all 10 vertices.
What is the inradius of a regular decagon?
The inradius (r), or apothem, of a regular decagon with side length a is r = a / (2 x tan(pi/10)) = a / (2 x tan(18 deg)). This is the radius of the inscribed circle tangent to all 10 sides and is the perpendicular distance from the center to any side.
Is this decagon tool free to use?
Yes, all calculators on Calculy including the decagon calculator are completely free to use with no registration or download required.