June 26, 2019
A regular hexagon is a polygon with six equal sides and angles.
The triangles formed by joining the center with all the vertices, are equal in size and are equilateral.
Angles of the Hexagon
The sum of interior angles of a hexagon = (6 − 2) · 180° = 720°
The value of an interior angle of the regular hexagon is 720º/6 = 120º
The central angle of the regular hexagon measures: 360º : 6 = 60º
Diagonals of the Hexagon
The number of diagonals = 6 · (6 − 3) : 2 = 9
Apothem of a Regular Hexagon
By applying the Pythagorean theorem for one of the triangles, we obtain:
Perimeter of a Regular Hexagon
Perimeter = 6 · l
Area of a Regular Hexagon
Calculate the apothem, perimeter and area of a regular hexagon inscribed in a circle with a radius of 4 cm.
P = 6 · 4 = 24 cm
The area of a square is 2,304 cm². Calculate the area of a regular hexagon that has the same perimeter as this square.