To this, the regular hexagon is point symmetric and rotationally symmetric at a rotation of 60° or multiples of this. All the sides opposite to each other are parallel. DIAGONALS OF A REGULAR POLYGON BJORN POONEN AND MICHAEL RUBINSTEIN Abstract. How many diagonals does a regular hexagon have? 9. The longest diagonals of a regular hexagon, connecting diametrically opposite vertices, are … It has 6 vertices. Another image of the hexagon on Saturn. Diagonal is a line from one vertices to another that is non adjacent. Congruent is all sides having the same lengths and angles measure the same. A hexagon has 9 diagonals. Similarly, substituting (n=5) for a pentagon we get the number of diagonals as 5. A regular hexagon has an exterior angle is of 60 degrees and the sum of all exterior angles is 360 degrees. Regular hexagon (a two-dimensional figure) is a polygon with six congruent sides. A regular hexagon contains six congruent sides and six congruent angles. 9 diagonals can be drawn inside a regular hexagon. C. 1 0. Circumcircle is a circle that passes through all the vertices of a two-dimensional figure. Regular Hexagon Properties. The number of diagonals in an n-sided polygon is given by . The number of diagonals of an n sided polygon is given by D n = 2 n (n − 3) A convex regular hexagon has 6 sides. Sum of interior angles equals 720°. It is made up of six equilateral triangles. B. We give a formula for the number of interior intersection points made by the diagonals of a regular n-gon. A regular hexagon has six rotational symmetries (rotational symmetry of order six) and six reflection symmetries (six lines of symmetry), making up the dihedral group D 6. Correct option is . 8. A regular hexagon has a total number of 9 diagonals. The only regular polygons that have all diagonals congruent are regular polygons with sides 4 and 5. The sum of all interior angles of a regular hexagon is 720 degrees. Interior angle is 120° and exterior angle is 60°. A octagon has 20 diagonals. These diagonals divide a hexagon into six congruent equilateral triangles, which means that their sides are all congruent and each of their angles are $ 60^{\circ}$. (A 4-sided regular polygon is a square). Hexagonal nuts and bolts are easy to grip with a wrench, which can be re-positioned every 60° if needed. The long diagonal is the line between two opposite vertices. A. Also, each interior angle is 120 degrees. nC2 - n (where n is the number of sides of the polygon) or in the expanded form: factorial (n) _____ {factorial (2) * factorial (n-2)} substituting (n = 6) for a hexagon we get the number of diagonals as 9. Long diagonals and bisecting lines coincide, they intersect with the median lines and with centroid, circumcircle and incircle center in one point. It has 6 equal sides and 6 equal angles. Answer. 9. 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