A regular n-gon has interior angles of (n − 2)·180°/n. Its area is half the perimeter times the apothem (the distance from the centre to a side), because it splits into n identical triangles.
Worked example: hexagon side 2
Step by step
- \text{interior angle} = \frac{(n-2)\cdot 180^\circ}{n} = 120^\circ
A regular 6-gon.
- P = n s = 12
Perimeter.
- a = \frac{s}{2\tan(\pi/n)} = \sqrt{3} \approx 1.7320
Apothem (centre to the middle of a side).
- A = \tfrac{1}{2} P a = 6 \sqrt{3} \approx 10.392
Area = half the perimeter times the apothem.
Reveal the answer
A = 6 \sqrt{3} \approx 10.392
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