A 2D closed polygon that is made up of 6 straight line segments is known as a hexagon. There are many concepts associated with it, such as construction, perimeter, and area of a hexagon. There are different classifications of hexagons based on the length of sides and the shape of the figure. In this article, we will take a detailed look at a few topics that fall under hexagons.
- Regular Hexagon: In such a type of hexagon, the length of the sides is equal. Additionally, the measure of all six angles is also equal. Thus, we can say that a regular hexagon is both equilateral and equiangular.
- Irregular Hexagon: A hexagon in which the six sides do not have equal measure is known as an irregular hexagon.
- Convex Hexagon: A hexagon in which all the interior angles are less than 180 degrees is known as a convex hexagon.
- Concave Hexagon: At least one of the angles of a hexagon should be greater than 180 degrees for it to be classified as a concave hexagon.
Properties of Regular Hexagons
- A hexagon always has six sides and six angles.
- All the side lengths are of the same measure, and the angles are also equal.
- A regular hexagon has nine diagonals.
- All the interior angles sum up to 720 degrees.
- Each interior angle is equal to 120 degrees.
- All the exterior angles sum up to 360 degrees.
- Each exterior angle measures 60 degrees.
Area of a Hexagon
The area of a hexagon can be defined as the two-dimensional space occupied by the figure or the region encompassed within the boundaries of that figure.
1. Using the Formula
The area of a regular hexagon can be calculated by using the following formula
Area = [3√3 s²]/2, where s is the length of the side.
2. Using the Apothem
There is another method that can be used to find the area of a hexagon. An apothem is a line drawn from the center of a hexagon to one of the sides at a right angle. Suppose you know the length of the apothem and the perimeter of the hexagon, then the formula for calculating the area is given as follows.
Area of a hexagon = ½ * perimeter * apothem
3. Coordinate method
Suppose you have an irregular hexagon and you know the coordinates of the vertices, then the area of the hexagon can be calculated. The steps to do this are listed below.
- Step 1: Multiply the x coordinate of one vertice with the y coordinate of the next one. Add all the results.
- Step 2: Multiply the y coordinate of one point with the x coordinate the next. Again add all the results.
- Step 3: Subtract the result of step 1 with step 2. You will have to take the modulus of the result. This gives you the area of the irregular hexagon.
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