What is a hexagon? A hexagon is a polygon with six sides and six vertices, which are the corners where two sides meet. The word hexagon comes from Greek, where 'hex' means six and 'gonia' means angle. In this figure, you can see a regular hexagon with its six sides and six vertices clearly labeled.
Hexagons can be classified in several ways. A regular hexagon has all sides of equal length and all interior angles equal to 120 degrees. An irregular hexagon has sides of different lengths or angles of different measures. Hexagons can also be convex, where all vertices point outward, or concave, where at least one vertex points inward. The blue hexagon is regular, the green one is irregular but still convex, and the red one is concave because one of its vertices points inward.
Let's explore the properties of a regular hexagon. Each interior angle of a regular hexagon measures 120 degrees, while each exterior angle is 60 degrees. The sum of all interior angles in any hexagon is 720 degrees, which can be calculated using the formula (n-2) times 180 degrees, where n is the number of sides. For a hexagon, that's (6-2) times 180, which equals 720 degrees. A hexagon has 9 diagonals in total, which are lines connecting non-adjacent vertices. These diagonals divide the hexagon into smaller triangles.
Now let's look at how to calculate the area and perimeter of a hexagon. For a regular hexagon with side length s, the area can be calculated using the formula: three times the square root of three, divided by two, multiplied by s squared. This formula comes from dividing the hexagon into six equilateral triangles. The perimeter is simply six times the side length, since all sides are equal in a regular hexagon. For example, if we have a regular hexagon with side length 2 units, the area would be approximately 10.39 square units, and the perimeter would be 12 units.
To summarize what we've learned: A hexagon is a polygon with six sides and six vertices. Regular hexagons have equal sides and interior angles of 120 degrees each. The area of a regular hexagon can be calculated using the formula three root three divided by two, multiplied by the square of the side length. The perimeter is simply six times the side length. Hexagons appear frequently in both nature and human designs due to their efficiency and aesthetic appeal. In nature, we see hexagons in honeycomb cells, which provide maximum storage space with minimal material. Snowflakes often exhibit six-fold symmetry based on the hexagonal crystal structure of ice. In human designs, hexagons are used for bolt heads to provide better grip, and in floor tiles and architectural elements for their pleasing geometric properties and ability to tessellate perfectly.