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Polygons

Interior angles, apothem and area of regular polygons.

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.

Ejemplo resuelto · hexagon side 2

Geometry · Polygons

Hexagon side 2

6,\ 2

Paso a paso

  1. \text{interior angle} = \frac{(n-2)\cdot 180^\circ}{n} = 120^\circ

    A regular 6-gon.

  2. P = n s = 12

    Perimeter.

  3. a = \frac{s}{2\tan(\pi/n)} = \sqrt{3} \approx 1.7320

    Apothem (centre to the middle of a side).

  4. A = \tfrac{1}{2} P a = 6 \sqrt{3} \approx 10.392

    Area = half the perimeter times the apothem.

Revelar la respuesta
A = 6 \sqrt{3} \approx 10.392

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Símbolos utilizados aquí

Toque cualquier símbolo para la definición completa, una imagen, y lo que cada letra en ella significa.

Cómo: Polygons

  1. A regular 6-gon.
  2. Perimeter.
  3. Apothem (centre to the middle of a side).
  4. Area = half the perimeter times the apothem.

Preguntas que la gente hace

Why does every triangle have angles adding to 180°?

Draw a line through one vertex parallel to the opposite side: the two alternate angles equal the other two angles of the triangle, and the three angles at the vertex lie on a straight line. That is Euclid's proof, and it is why the fact holds only on a flat plane.

When do I use the law of sines versus the law of cosines?

Cosines when you know three sides, or two sides and the angle between them. Sines when you know an angle and the side opposite it, plus one more piece.

What is the difference between area and perimeter?

Perimeter is the length of the boundary (one dimension, measured in metres); area is the amount of surface inside (two dimensions, square metres). Doubling every side doubles the perimeter but quadruples the area.

Más en Geometry

TrianglesPythagorean theoremCirclesSolidsCoordinate geometryEuclid's axioms and the structure of proofCongruent and similar trianglesCircle theoremsTransformations: translation, rotation, reflection, dilationSolid geometry: prisms, pyramids, spheres