Heptagon Area Calculator
Calculate the area of a regular heptagon (7-sided polygon) from side length, perimeter, or radius
Calculate Heptagon Area
Length of one side of the regular heptagon
Calculation Results
Area Formula
Exact formula: A = (7 × a²) / (4 × tan(π/7))
Simplified formula: A ≈ 3.633912444 × a²
Where: a = side length, A = area
Step-by-Step Example
Example: Heptagon with Side Length 6 cm
Step 1: Given side length (a) = 6 cm
Step 2: Apply the heptagon area formula
Formula: A = 3.633912444 × a²
Step 3: Substitute the values
Calculation: A = 3.633912444 × (6)²
Step 4: A = 3.633912444 × 36 = 130.82 cm²
Result: The area is approximately 130.82 cm²
Alternative Input Methods
From Perimeter: If P = 42 cm, then a = P/7 = 42/7 = 6 cm
From Circumradius: If R = 6.61 cm, then a = R × 2 × sin(π/7) ≈ 6 cm
From Inradius: If r = 5.58 cm, then a = r × 2 × tan(π/7) ≈ 6 cm
Heptagon Area Facts
Seven-Sided
A heptagon has exactly 7 equal sides
Area Coefficient
Multiply side² by 3.634 for quick area calculation
Trigonometric
Uses tan(π/7) ≈ 0.4816 in exact formula
Input Methods
Side Length
Direct measurement of one side
Perimeter
Total distance around (P = 7 × a)
Circumradius
Radius of circumscribed circle
Inradius
Radius of inscribed circle (apothem)
Quick Tips
Heptagon is also called septagon
Area formula works only for regular heptagons
Multiply side² by 3.634 for quick estimation
Rarely used in design due to odd number of sides
Understanding Heptagon Area Calculation
What is a Heptagon?
A heptagon (also called septagon) is a seven-sided polygon. In a regular heptagon, all sides have equal length and all interior angles are equal (approximately 128.57°). Despite being geometrically interesting, heptagons are rarely used in practical design due to their odd number of sides.
Area Formula Derivation
The heptagon area formula comes from the general regular polygon area formula:
A = (n × a²) / (4 × tan(π/n))
For a heptagon (n = 7), this becomes: A = (7 × a²) / (4 × tan(π/7)) ≈ 3.634 × a²
Conversion Formulas
From Perimeter
a = P / 7
From Circumradius
a = R × 2 × sin(π/7)
From Inradius
a = r × 2 × tan(π/7)
Area Formula
A = 3.633912444 × a²
Note: All formulas assume a regular (equilateral and equiangular) heptagon.
Real-World Applications
Architectural Design
Occasional use in decorative patterns and unique building designs
Mathematical Study
Educational purposes and geometric theorem exploration
Game Design
Board games and puzzle design with unique symmetries