Introduction, Angles, Diagonals, Properties, Formula & Solved Questions

A hexagon which is an equilateral as well as an equiangular is called a Regular hexagon. A Regular hexagon is bi-centric, which indicates that it’s both; cyclic and tangential i.e., it has an inscribed circle & a circumscribed circle. 

It is a 6-side polygon different from an irregular hexagon. A Regular hexagon consist six rotational symmetries along with six reflection symmetries i.e., all six sides & edges of hexagon are equal.

Check Solution for Class 8 Chapter 3 Understanding Quadrilaterals

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What is Regular Hexagon?

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A regular hexagon is a polygon;

• Have six equal sides, which means having equal six sides mean all equal angles,
• “Hex” means six which represent sides, i.e., six sides shape,
• Lengths & measurement of all the sides are equal & it has a convex geometrical shape,
• All the points of a regular hexagon point outwards,
• There are total 9 diagonals,
• The sum of all interior angles will be 720 degrees & exterior angles will be 360 degrees, 
• Each interior angle will be 120 degrees, & each exterior angle will be 60 degrees,
• The area will be the region occupied by hexagon inside its boundary,
• The perimeter of hexagon will be the total length of all 6 sides,
• The triangles formed by joining the centre with all the vertices, are equal in size and are equilateral.

Check Important Difference Between Square and Rhombus

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How to draw a Regular Hexagon?

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A regular hexagon is easy to draw. One only need compass, rules & pen/pencil & should follow the steps below;

1. Draw a linear segment whose length will be the hexagon side length,
2. Construct a circle, its centre should be at one end of the linear segment and radius should be equal to the segment length,
3. A second circle should be constructed without changing the radius, & its centre should be at the other end of the linear segment. The two points are defined where this circle intersects with the first one.
4. With the help of the same radius, construct a new circle placing the tip of the compass on the last defined point,
5. A new point will be defined as it intersects with the first circle.
6. Repeat this procedure for two more times i.e., Place the tip of the compass on the last point and construct another circle,
7. There will be a total of six points around the first circle,
8. These points will become the vertices of the hexagon,
9. At last, Draw linear segments between them,
10. Regular hexagon is created.

Check Important Notes for Properties of Hexagon

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Angles of the regular hexagon

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• The sum of all the angles of a regular hexagon is equal to 720,
• There are total six sides in a regular hexagon,
• The sum of interior angles of a regular hexagon = (6-2) x 180 degrees = 720 degrees,
• The value of an interior angle of the regular hexagon is = 720/6 degrees =120 degrees,
• The central angle of the regular hexagon measures: 360:6 degrees =60 degrees.

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Diagonals of the Regular Hexagon

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• A diagonal is known as a line that joins two non-adjacent vertices. A regular hexagon has a total of 9 diagonals,
• The total number of diagonals = 6 x (6-3): 2 = 9

Also Check:

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Formulas for the Regular Hexagon

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1] Area of a Regular Hexagon-

Divide the regular hexagon into small six isosceles triangles. Then find the area of the triangles one by one multiply it by 6 to find the total area of the polygon.

FORMULA: 

A = 3(√3/2)a²

Three different ways to find out the area are as follows:

1. When the length of the side of a regular hexagon is given, the formula will be:

Area = s²n/4 tan (180/n)

Where, s = length of the side & n = number of the side.

2. When the radius (circumradius) is given, the formula will be:

Area = r²n sin (360/n)/2

Where, r = radius (circumradius) & n = number of the side

3. When the apothem (in radius) is given, the formula will be:

Area = a²n tan (180/n)

Where, a = length of the apothem & n = number of the side

2] Perimeter of a Regular Hexagon-

It can be determined by calculating the sum of all the six sides of a regular hexagon. The perimeter will be the sum of all 6 side lengths of the hexagon. The perimeter of a hexagon is given by:

FORMULA: 

P = 6a

Where, a = sides of regular hexagon.

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Things to Remember

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• It has 6 vertices with 6 equal sides and 6 equal angles,
• It constitutes of six equilateral triangles,
• The hexagon’s radius is equal to the length of its sides,
• The interior angles are 120° of regular hexagon,
• The exterior angles of a regular hexagon are 60°,
• Sum of interior angle is 720°,
• A regular Hexagon has 9 diagonals.
• All the sides opposite to each other are parallel in nature.

Check Also: Quadrilateral Angle Sum Property

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