Last updated on July 31st, 2025
A hexagon is a 2-dimensional shape with six sides. The surface area of a hexagon refers to the total area covered by its shape. In this article, we will learn about the surface area of a hexagon and how to calculate it.
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.
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.
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.
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.
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.
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.
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.
Perimeter = 42 cm
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.
Total Area = 45 cm²
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.
Area = 64.95 cm²
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.
Side length = 8 cm
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.
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