How to Calculate the Square Footage of a Regular Decagon
A regular decagon is a ten-sided polygon with all sides and angles equal. Like the heptagon, it is an uncommon shape that custom builders reach for in gazebos, rotundas and decorative features. Its near-circular outline makes it a popular compromise between a polygon's straight, buildable edges and a circle's smooth look. Because it is regular, one side length determines the whole area.
The regular decagon formula
For a regular decagon with side length s:
Area = (10 × s²) ⁄ (4 × tan(π ⁄ 10))
As with any regular polygon, the shape is divided into ten identical triangles meeting at the center, and the tangent term accounts for their geometry. Enter a single side length above and the calculator does the rest.
Measuring a decagon
Measure any one side from corner to corner with the tape held flat and straight. Since all ten sides are equal on a regular decagon, that one measurement is all the area calculation needs. Checking a second side confirms the shape is genuinely regular; if sides vary, treat it as an irregular polygon and divide it into triangles.
Worked example
For a decagonal gazebo floor with 10-foot sides:
Area = (10 × 10²) ⁄ (4 × tan(π ⁄ 10)) = 1000 ⁄ (4 × 0.3249) ≈ 769.42 square feet.
That is a sizeable floor; for decking or tile, a 10–15% waste allowance covers the numerous angled perimeter cuts, suggesting roughly 846–885 square feet of material.
Where ten-sided shapes appear
- Gazebos and pavilions: Ten facets approximate a round building while keeping straight, framable walls.
- Rotundas and feature rooms: Decagonal floors appear in formal architecture.
- Planters and decorative beds: A ten-sided raised bed reads almost circular but is easier to build from straight timber.
Related shape calculators
For nearby polygon counts, use the octagon (8 sides), heptagon (7 sides) or hexagon (6 sides) calculators. If you ultimately want a truly round area, compare with the circle calculator.