Area of Hexagon

A hexagon is a polygon with six sides and six angles. When all its sides are of equal length, it is known as a regular hexagon. The area of a hexagon is the total space it encloses.

To find the area of a regular hexagon, we use the formula: (3√3/2) × s², where s is the length of a side. Now let’s see how the formula is derived.

Derivation of the formula: A regular hexagon can be divided into six equilateral triangles. The area of one equilateral triangle is (√3/4) × s². Since there are six such triangles in a hexagon, the total area will be 6 × (√3/4) × s². Simplifying this gives us the area of a hexagon: (3√3/2) × s². Therefore, the area of a hexagon = (3√3/2) × s².

We can find the area of a regular hexagon using the formula with the side length. The area can also be found using the apothem and perimeter:

Method using the side length

If the side length 's' is given, the area of a regular hexagon is found using the formula Area = (3√3/2) × s². For example, if the side length is 6 cm, what will be the area of the hexagon? Area = (3√3/2) × 6² = (3√3/2) × 36 = 93.53 cm² (approx.)

Method using the apothem and perimeter

If the apothem 'a' and perimeter 'P' are given, the area of the hexagon is found using the formula Area = (1/2) × a × P. For example, if a = 10 cm and P = 60 cm, what will be the area of the hexagon? Area = (1/2) × 10 × 60 = 300 cm².

We measure the area of a hexagon in square units. The measurement depends on the system used: In the metric system, the area is measured in square meters (m²), square centimeters (cm²), and square millimeters (mm²). In the imperial system, the area is measured in square inches (in²), square feet (ft²), and square yards (yd²).

Since a regular hexagon can be divided into six equilateral triangles, there are two principal methods by which the area can be calculated. Take a look at the special cases:

Case 1: Use of Side Length If the side length is given, use the formula Area = (3√3/2) × s², where s is the side length.

Case 2: Use of Apothem and Perimeter If the apothem and perimeter are given, use the formula Area = (1/2) × a × P, where a is the apothem and P is the perimeter.

To ensure correct results while calculating the area of a hexagon, there are some tips and tricks you should know about. Here are some:

• The apothem is the perpendicular distance from the center to a side of the hexagon.
   
• The area can be calculated in two ways, depending on the information provided.
   
• There are formulas to find the area when the side length or the apothem and perimeter are given.
   
• Always verify if the hexagon is regular (all sides and angles are equal) before using the regular hexagon formulas.

• Area: The total space occupied by a shape. It tells us how much surface a shape covers.

• Hexagon: A polygon with six sides and six angles.

• Regular Hexagon: A hexagon in which all sides and angles are equal.

• Apothem: The perpendicular distance from the center of the hexagon to one of its sides.

• Perimeter: The total length around a hexagon, calculated by adding the length of all its sides.