A hexagon is a polygon with 6 sides and 6 angles, (hexa- means six). In the figure below are 3 different species of hexagons.

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A hexagon is a form that is commonly seen in everyday life. The shapes that consist of a honeycomb, a nut, and bolts space all examples of genuine life objects in the form of hexagon.

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Hexagon classifications

Like various other polygons, a hexagon have the right to be classified as regular or irregular. If all the sides and interior angle of a hexagon room equal, it is a constant hexagon. Otherwise that is an irregular hexagon.

Regular hexagonIrregular hexagon
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All sides and also interior angles space equalNot all sides and also angles are equal

Hexagons or various other polygons can likewise be classified as either convex or concave. If all inner angles of a hexagon or polygon are much less than 180°, it is convex. If one or an ext interior angle are larger than 180°, the is concave. A consistent hexagon is constantly a convex hexagon.

Convex hexagonConcave hexagon
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All inner angles 180°

Diagonals of hexagon

A diagonal line is a heat segment joining 2 non-consecutive vertices. Three diagonals have the right to be drawn from each vertex. A total of nine diagonals have the right to be attracted for a hexagon. The following figure is an example.

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Internal angle of a hexagon

The amount of the inner angles the a hexagon amounts to 720°.

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As presented in the number above, three diagonals have the right to be drawn to division the hexagon into 4 triangles. The blue lines over show simply one means to division the hexagon into triangles; there room others. The amount of interior angles the the 4 triangles equates to the sum of interior angles of the hexagon. Because the sum of the inner angles the a triangle is 180°, the amount of the inner angles the the hexagon is 4 × 180° = 720°.

Regular hexagon

A regular hexagon is a hexagon in which all sides have equal length and also all inner angles have equal measure.

Angles and sides that a constant hexagon

Since every of the six internal angles in a consistent hexagon are equal in measure, each interior angle procedures 720°/6 = 120°, as displayed below.

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Each exterior edge of a constant hexagon has actually an same measure that 60°.

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Sides that a continuous hexagon room equal in length and also opposite sides space parallel.

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Symmetry in a regular hexagon

A consistent hexagon has actually 6 present of symmetry and also a rotational the contrary of stimulate 6, which method that it have the right to be rotated in together a method that it will certainly look the exact same as the original shape 6 times in 360°.

Lines that symmetryRotational symmetry
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6 lines of symmetrySix 60° angles of rotation

Area that a regular hexagon

The area that a regular hexagon v side size s is:

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From the center, a constant hexagon have the right to be divided into six equilateral triangles, each having actually side length, s, as shown below.

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The area, T, of one of the it is provided triangles, attracted in blue, can be discovered by utilizing

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, where the apothem is the height of the triangle. Since there are six equilateral triangles, the area the a continual hexagon is
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.