Regular Hexagon Definition Properties and Area Formula

The concept of regular hexagon plays a key role in mathematics and is widely applicable in geometry, problem solving, and real-world situations such as tiling, patterns, and engineering. Regular hexagons are especially important for students in exams and maths competitions due to their symmetry and useful formulas.

What Is a Regular Hexagon?

A regular hexagon is a six-sided polygon where all the sides are equal in length and all the internal angles are the same—each measuring 120°. You’ll find this concept applied in geometry, coordinate geometry, and even nature (like in honeycombs). Regular hexagons are a special type of polygon with high symmetry and unique properties among 2D shapes.

Key Formula for Regular Hexagon

Here’s the standard formula for the area and perimeter of a regular hexagon with side length \( a \):

• Area:  \( \text{Area} = \frac{3\sqrt{3}}{2} a^2 \)
• Perimeter:  \( \text{Perimeter} = 6a \)
• Number of Diagonals:  \( \text{Diagonals} = \frac{6(6-3)}{2} = 9 \)

You can find more geometry shape formulas in Vedantu’s formula sheet.

Properties of Regular Hexagon

Property	Value
Number of sides	6 (equal)
Internal angle	120° each
Sum of internal angles	720°
Lines of symmetry	6
Diagonals	9
Tessellation	Yes (tiles plane without gaps)

Difference Between Regular and Irregular Hexagons

Regular Hexagon	Irregular Hexagon
All sides & angles are equal	Sides or angles differ in length/degree
Area formula: \( \frac{3\sqrt{3}}{2} a^2 \)	Area found by dividing into triangles etc.
6 lines of symmetry	May have 0, 1, or more lines of symmetry
Tessellates perfectly	Usually does not tessellate

How to Draw a Regular Hexagon

1. Draw a circle using a compass; mark the center as O.
2. Place the compass pointer at a point A on the circle and without changing the radius, step around the circle marking points B, C, D, E, and F.
3. Join each consecutive point: AB, BC, CD, DE, EF, and FA. This forms a regular hexagon.

Each side equals the radius of the circle. This construction is standard for geometry classes and projects.

Solved Example: Area of a Regular Hexagon

Question: Find the area of a regular hexagon with side length 5 cm.

Solution:

1. Area formula = \( \frac{3\sqrt{3}}{2} a^2 \ )

2. Substitute \( a = 5 \) cm: \( \frac{3\sqrt{3}}{2} \times 5^2 \ )

3. Calculate: \( \frac{3\sqrt{3}}{2} \times 25 \ )

4. \( = \frac{75\sqrt{3}}{2} \) cm²

5. If \( \sqrt{3} \approx 1.73 \), then \( \frac{75 \times 1.73}{2} = \frac{129.75}{2} = 64.88 \) cm²

6. Final Answer: Area ≈ 64.9 cm²

Step-by-Step: Find Perimeter and Diagonals

Question: Find the perimeter and number of diagonals of a regular hexagon with side 7 m.

Solution:

1. Perimeter = 6 × 7 = 42 m

2. Number of diagonals = \( \frac{6(6-3)}{2} = 9 \)

3. Final Answers: Perimeter = 42 m; Diagonals = 9

Speed Trick for Regular Hexagon Area

Use this Vedic shortcut: The area of a regular hexagon = ( 2.598 ) × side² (using approximate value for \( \frac{3\sqrt{3}}{2} \)). For quick math, just multiply side × side × 2.6!

Example: Side = 10 cm → 10 × 10 × 2.6 = 260 cm² (quick estimate).

Such tricks help in MCQs and competitions. Vedantu’s live classes offer more time-saving hacks for geometry.

Common Errors with Regular Hexagon

• Mixing up formulas with other polygons (like pentagon or square).
• Using wrong side length for area (not squared), or not multiplying by 2.6 in quick tricks.
• Forgetting all internal angles are equal.

Real-Life Uses of Regular Hexagon

Regular hexagons are seen in nature and daily life—beehive cells, some floor tiles, nuts and bolts, snowflakes, and even football patterns. Their symmetry makes them ideal for strong, space-filling designs. To learn about how shapes tessellate, see our tessellation guide.

Connection to Other Maths Topics

Understanding the regular hexagon helps you master advanced concepts like regular polygons, symmetry, and triangle properties (a hexagon is made of six equilateral triangles). It’s closely linked to area formulas, coordinate geometry, and trigonometry.

Classroom Memory Tip

A memorable way: “Hexagon” = “six angles, six sides, all same,” and its area formula starts with a 3 and root 3 for quick recall. Vedantu teachers teach such mnemonics with stories and patterns kids remember!

Try These Yourself

• Calculate the perimeter of a regular hexagon of side 8 cm.
• Find the area of a regular hexagon with side 4 m (use shortcut!).
• Draw and label all diagonals of a regular hexagon.
• List 3 places you see hexagons in real life.

We explored regular hexagon—from definition, properties, formula, examples, and memory tricks to real-world uses. Keep practicing with Vedantu’s maths resources and live classes—soon, hexagons will be your shortcut to scoring high in Maths!

• Hexagon: Sides & Angles
• Regular Polygon: Properties & Formulas
• Area of Geometric Shapes
• Tessellation in Maths
• Properties of Triangle