5/19/2023 0 Comments Perfect hexagonIt is tangent to all six sides and its center coincides with the center of the circumcircle. This circle is called inscribed circle or incircle. The radius of circumcircle R_c is usually called circumradius.Īnother circle can also be drawn, that passes through the middles of the hexagon sides. Likewise, the diagonals of the hexagon are diameters of the circumcircle. This is the cirmuscribed circle or circumcircle of the polygon. The center of this circle is the center of the hexagon. Circumcircle and incircleĪs happens with any regular polygon, a circle that passes through all six vertices of the hexagon can be drawn. The regular hexagon is composed by six identical equilateral triangles having a common vertex, the polygon centre. Half of them are passing through diagonally opposite vertices and the remaining through the middles of opposite edges. The regular hexagon features six axes of symmetry. The diagonals of a hexagon separate its interior into 4 triangles Properties of regular hexagons Symmetry Since he sum of internal angles in one triangle is 180°, 4 triangles, side by side, should measure up to 4x180=720°. This can be easily be concluded by counting the number of triangles fitting inside the hexagon, by connecting its vertices (avoiding intersections). The sum of the internal angles of any hexagon, either convex or concave is always 720°. Any hexagon that is not regular is called irregular. As demonstrated in the figure below, many possible concave hexagons can be defined, with equal sides, but unequal interior angles (these are called equilateral). Unlike the triangle, having the sides equal does not imply that the interior angles are also equal, since the hexagon may be concave. A hexagon is called regular when all of its sides and interior angles are equal. To the contrary, a concave hexagon (or polygon) has one or more of its interior angles greater than 180°. When convex, a hexagon (or a polygon in general) has none of its interior angles greater than 180°. Like any polygon, a hexagon can be either convex or concave, as illustrated in the next figure. Hexagon is a polygon with six sides and six vertices.
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