How this calculator works
Connect the centre to all seven vertices. Each resulting triangle has base equal to a polygon side and height equal to the apothem. Add those seven areas. The running-area table shows that decomposition, and the scaling table shows why enlarging a side by a factor k multiplies area by k². A target-area input reverses the side-based formula. Perimeter and either radius determine the same regular shape, so they can also be used as starting measurements.
Formula
A = 7ar/2 = 7a²/[4tan(π/7)] = 7R²sin(2π/7)/2 = 7r²tan(π/7). For target area A, a = sqrt(4A tan(π/7)/7). P=7a. Scaling a by k scales A by k².
Worked example
A regular heptagon with side 2 m has area about 14.53564978 m². Each of its seven central triangles contributes about 2.07652140 m². A target area of 58.14259910 m² requires side 4 m, twice the original side.
Frequently asked questions
Can I use an irregular heptagon?
No. Seven equal central triangles require a regular polygon. For an irregular outline, enter its vertex coordinates in an irregular-polygon tool.
Which radius is the triangle height?
The apothem, or inradius, reaches the midpoint of a side at right angles. The circumradius reaches a vertex and is longer.
Why does doubling the side quadruple area?
Both the base and height of each central triangle double. Their product therefore becomes four times as large.