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Geometry · Polygons

Pentagon side 1

5,\ 1

Step by step

  1. \text{interior angle} = \frac{(n-2)\cdot 180^\circ}{n} = 108^\circ

    A regular 5-gon.

  2. P = n s = 5

    Perimeter.

  3. a = \frac{s}{2\tan(\pi/n)} = \frac{1}{2 \sqrt{5 - 2 \sqrt{5}}} \approx 0.68819

    Apothem (centre to the middle of a side).

  4. A = \tfrac{1}{2} P a = \frac{5}{4 \sqrt{5 - 2 \sqrt{5}}} \approx 1.7205

    Area = half the perimeter times the apothem.

Reveal the answer
A = \frac{5}{4 \sqrt{5 - 2 \sqrt{5}}} \approx 1.7205