Numbers · geometry · regular polygonArea of a regular polygon — formula and calculator
Work out the area of a regular polygon with the formula S = n·a² / (4 tan(180° / n)) — your numbers substituted and a diagram drawn. The perimeter is calculated too. Units can be mixed, and the answer comes in the units you need, hectares and acres included.
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Calculator
enter the sizes — the formula and diagram follow02
Formula
and what each letter meansArea
S = n·a² / (4 tan(180° / n))
Perimeter
P = n × a
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Worked example
with real numbersGivenn = 6, a = 4 cm
Solution
S = n·a² / (4 tan(180° / n)) = 6 × 4² / (4 × tan(180° / 6)) = 41.5692 cm²
P = n × a = 6 × 4 = 24 cm
Answer: area — 41.57 cm², perimeter — 24 cm.
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Common mistakes
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Nearby shapes
SquareS = a²RhombusS = d₁ × d₂ / 2PrismV = S₀ × hCalculatorAll 19 shapes, the composite shape and hectares →
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