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308 LearnersLast updated on August 5, 2025
Surface Area of Hexagon
What is the Surface Area of a Hexagon?
The surface area of a hexagon is the total area occupied by its boundary or surface. It is measured in square units.
A hexagon is a flat, six-sided polygon with six angles. Regular hexagons are polygons where all sides and angles are equal, while irregular hexagons have sides and angles of different lengths and degrees.
The surface area of a hexagon typically refers to the area within its six sides.
Surface Area of a Hexagon Formula
A hexagon can be regular or irregular, and the formula to calculate the area differs accordingly.
For a regular hexagon, the area can be calculated using the formula: Area = (3√3/2) × s² Where s is the length of one side of the hexagon.
For irregular hexagons, the area can be determined by dividing it into simpler shapes, like triangles, and calculating their combined areas.
Regular Hexagon Area
The area of a regular hexagon, where all sides are equal, can be calculated using the formula:
Area = (3√3/2) × s² square units
Here, s is the length of one side. This formula arises because a regular hexagon can be divided into six equilateral triangles.
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Irregular Hexagon Area
To find the area of an irregular hexagon, divide it into simpler shapes such as triangles or rectangles, calculate the area of each shape, and then sum them up. There is no single formula for an irregular hexagon, as it depends on the dimensions and organization of the simpler shapes.
Perimeter of a Hexagon
The perimeter of a hexagon is the total length of its outer boundary.
For a regular hexagon, the perimeter is calculated by multiplying the length of one side by six:
Perimeter = 6 × s
Where s is the length of one side. For an irregular hexagon, add the lengths of all six sides.
Confusion between Regular and Irregular Hexagons
Students may assume that all hexagons are regular. Always verify if the hexagon is regular (all sides and angles equal) or irregular, as the approach to finding the area differs.
Mistake 1
Incorrect Division of Irregular Hexagons
When dividing an irregular hexagon into simpler shapes, incorrect division can lead to errors. Ensure the division results in shapes with calculable areas, like triangles or rectangles.
Mistake 2
Misapplying the Regular Hexagon Formula
Some students may apply the regular hexagon formula to an irregular hexagon. Confirm the hexagon type before using the formula for regular hexagons.
Mistake 3
Neglecting Unit Consistency
Ensure all measurements are in the same unit before calculating the area to avoid miscalculations. Convert units if necessary.
Mistake 5
Solved Examples of Surface Area of Hexagon
Find the area of a regular hexagon with a side length of 4 cm.
Area = 41.57 cm²
Problem 1
Given s = 4 cm. Use the formula: Area = (3√3/2) × s² = (3√3/2) × 4² = (3√3/2) × 16 = 41.57 cm²
A regular hexagon has a side length of 7 cm. Find its perimeter.
Explanation
Perimeter = 42 cm
Problem 2
Use the formula: Perimeter = 6 × s = 6 × 7 = 42 cm
An irregular hexagon is divided into two triangles and one rectangle. The triangles have areas of 10 cm² and 15 cm², and the rectangle has an area of 20 cm². Find the total area of the hexagon.
Explanation
Total Area = 45 cm²
Problem 3
Sum the areas of the simpler shapes: Total Area = 10 + 15 + 20 = 45 cm²
Find the area of a regular hexagon with a side length of 5 cm.
Explanation
Area = 64.95 cm²
Problem 4
Area = (3√3/2) × s² = (3√3/2) × 5² = (3√3/2) × 25 = 64.95 cm²
If the perimeter of a regular hexagon is 48 cm, find the length of one side.
Explanation
Side length = 8 cm
It is the total area enclosed within the six sides of the hexagon.
1.What formulas are used to find the surface area of a hexagon?
2.What is the difference between regular and irregular hexagons?
3.Can a hexagon be divided into triangles to find its area?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of a Hexagon
Students often make mistakes while calculating the surface area of a hexagon, leading to incorrect answers. Below are some common mistakes and ways to avoid them.
Nishtha Tiwari
About the Author
Nishtha is a passionate Maths teacher with 3 years of teaching experience. She focuses on making mathematics simple, engaging, and stress-free through student-centric, interactive, and exam-oriented teaching. With strong fundamentals, regular practice, an
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