Asked by Damianah Joy Locher
What is a Heptagon?
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Answered by
GPT-5 mini
AI
A heptagon is a polygon with seven sides and seven angles. It’s also sometimes called a septagon.
Key facts (regular heptagon = all sides and angles equal)
- Sum of interior angles: (7−2)×180° = 900°.
- Each interior angle (regular): 900°/7 ≈ 128.571°.
- Each exterior (central) angle: 360°/7 ≈ 51.429°.
- Number of diagonals: 7(7−3)/2 = 14.
- Circumradius (for side length a): R = a / (2 sin(π/7)).
- Apothem/inradius: r = a / (2 tan(π/7)).
- Area (regular): A = (7/4) a^2 cot(π/7) = (7a r)/2.
Note: a regular heptagon cannot be constructed exactly with just straightedge and compass.
Key facts (regular heptagon = all sides and angles equal)
- Sum of interior angles: (7−2)×180° = 900°.
- Each interior angle (regular): 900°/7 ≈ 128.571°.
- Each exterior (central) angle: 360°/7 ≈ 51.429°.
- Number of diagonals: 7(7−3)/2 = 14.
- Circumradius (for side length a): R = a / (2 sin(π/7)).
- Apothem/inradius: r = a / (2 tan(π/7)).
- Area (regular): A = (7/4) a^2 cot(π/7) = (7a r)/2.
Note: a regular heptagon cannot be constructed exactly with just straightedge and compass.
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