Calculate area, perimeter, diagonal, inradius, and circumradius of a regular pentagon from side length.
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Result
Total area of a regular pentagon with side length 6.
About the diagonal
The diagonal of a regular pentagon equals the side length multiplied by the golden ratio (1.618...), connecting the deep relationship between pentagons and the golden ratio.
Geometry
The pentagon calculator computes area, perimeter, diagonal, inradius, and circumradius of a regular pentagon from its side length. This page also explains the main assumptions behind the regular pentagon properties from side length result, highlights the supporting figures shown by the calculator, and helps the reader use the estimate without overstating what a quick online tool can prove.
A regular pentagon has five equal sides and internal angles of 108 degrees. The diagonal-to-side ratio equals the golden ratio (1 + sqrt(5))/2 ≈ 1.618.
Area = (s^2 * sqrt(25 + 10*sqrt(5))) / 4. Perimeter = 5s. This regular pentagon properties from side length formula explanation shows how the entered values flow into the main result and the supporting figures the calculator returns.
This calculator handles regular pentagons only. This added context connects the displayed result to the assumptions, method, and practical interpretation shown elsewhere on the page.
A worked example helps translate the regular pentagon properties from side length maths into a realistic scenario so the user can compare the headline result with a concrete set of inputs.
That matters because a result is easier to trust when the page shows how the same logic behaves in a practical case instead of leaving the formula abstract.
Frequently asked questions
In a regular pentagon, the diagonal divided by the side length equals the golden ratio phi ≈ 1.618. This makes pentagons fundamental to golden-ratio geometry.
108 degrees. (5-2) * 180 / 5 = 108. The page uses this rule as a quick reference, but the surrounding assumptions and units still matter when you interpret the result.
The safest manual check is to follow the same formula or rule one step at a time and compare that working with the calculator output. That catches sign errors, bracket mistakes, and input-order mixups without requiring any extra method beyond the underlying maths itself.
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