A hexagon is a closed 2D shape that is made up of straight lines. It is a two-dimensional shape with six sides, six vertices, and six edges. The name is divided into hex, which means six, and gonia, which means corners.
|2.||Types of Hexagon|
|3.||Properties of a Hexagon|
|5.||FAQs on Hexagon|
Hexagon is a two-dimensional geometrical shape that is made of six sides, having the same or different dimensions of length. Some real-life examples of the hexagon are a hexagonal floor tile, pencil, clock, a honeycomb, etc. A hexagon is either regular(with 6 equal side lengths and angles) or irregular(with 6 unequal side lengths and angles).
Types of Hexagon
Hexagons can be classified based on their side lengths and internal angles. Considering the sides and angles of a hexagon, the types of the hexagon are,
- Regular Hexagon: A regular hexagon is one that has equal sides and angles. All the internal angles of a regular hexagon are 120°. The exterior angles measure 60°. The sum of the interior angles of a regular hexagon is 6 times 120°, which is equal to 720°. The sum of the exterior angles is equal to 6 times 60°, which is equal to 360°.
- Irregular Hexagon: An irregular hexagon has sides and angles of different measurements. All the internal angles are not equal to 120°. But, the sum of all interior angles is the same, i.e 720 degrees.
- Convex Hexagon: A convex hexagon is one in which all the interior angles measure less than 180°. Convex hexagons can be regular or irregular, which means they can have equal or unequal side lengths and angles. All the vertices of the convex hexagon are pointed outwards.
- Concave Hexagon: A concave hexagon is one in which at least one of the interior angles is greater than 180°. There is at least one vertex that points inwards.
Properties of Hexagon
A hexagon is a flat two-dimensional shape with six sides. It may or may not have equal sides and angles. Based on these facts, the important properties of a hexagon are as follows.
- It has six sides, six edges, and six vertices
- All the side lengths are equal or unequal in measurement
- All the internal angles are equal to 120° in a regular hexagon
- The sum of the internal angles is always equal to 720°
- All the external angles are equal to 60° in a regular hexagon
- Sum of the exterior angles is equal to 360° in a hexagon
- The number of diagonals (a line segment joining two vertices of a polygon) that can be drawn is 9
- A regular hexagon is also a convex hexagon since all its internal angles are less than 180°
- A regular hexagon can be split into six equilateral triangles
- A regular hexagon is symmetrical as each of its side lengths is equal
- The opposite sides of a regular hexagon are always parallel to each other.
As with any polygon, a regular hexagon also has a different formula to calculate the area, perimeter, and a number of diagonals. Let us look into each one of them.
Diagonals of a Hexagon
A diagonal is a segment of a line, that connects any two non-adjacent vertices of a polygon. The number of diagonals of a polygon is given by n(n-3)/2, where 'n' is the number of sides of a polygon. The number of diagonals in a hexagon is given by, 6 (6 - 3) / 2 = 6(3)/2, which is 9. Out of the 9 diagonals, 6 of them pass through the center of the hexagon.
Sum of Interior Angles of Hexagon
The sum of internal angles formed by a regular hexagon is 720˚ (because each angle is 120˚ and there are 6 such angles adding up to 720˚). It is given by the formula for regular polygon, where n is a number of sides, which has a value of 6 for hexagonal shape. The formula is (n-2) × 180°. Therefore, (6-2) ×180° which gives us 720°.
Area of a Regular Hexagon
The area of a regular hexagon is the space or the region occupied by the shape. It is measured in square units. Let us divide the hexagon into 6 equilateral triangles as shown below. Let us calculate the area of one triangle and multiply it by 6 to get the entire area of the hexagon.
Area of one equilateral triangle is √3a2/4 square units. Hence, the area of a regular hexagon formed by combining 6 such triangles is,
6 × √3a2/4
= 3√3a2/2 square units
Therefore, the formula for the regular hexagon area is 3√3a2/2 square units.
Perimeter of a Hexagon
Perimeter is the total length of the boundary or the outline of a shape. Considering the side of a regular hexagon as 'a' units, the regular hexagon perimeter is given by summing up the length of all the sides which is equal to 6a units. Therefore, the perimeter of a regular hexagon = 6a units, and the perimeter of an irregular hexagon = (a + b + c + d + e + f) units, where, a, b, c, d, e, and f are the side-lengths of the hexagon.
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Example 1: What is the area of a regular hexagon with sides equal to 3 units?
Area of a regular hexagon = 3√3a2/2 square units.
Given side 'a' = 3 units
Therefore, area = 3(√3)32/2
= (3 × √3 × 9) /2
= (27× √3) / 2
= 23.382 square units,
Example 2: Find the length of each side of a regular hexagon, if the hexagon's area is 150√3 square units. Use the length of the sides to find the perimeter of the hexagon.
Applying the formula of area of a regular hexagon,
Area of a regular hexagon = 3√3a2/2 square units.
Therefore, 150√3 = 3√3a2/2
300√3 = 3√3a2
Canceling √3 on both sides,
300/3 = a2
100 = a2
a = √100
Therefore, the length of each side, a = 10 units.
Therefore, the length of the sides of the hexagon = 10 units.
Perimeter of a regular hexagon = 6a units.
a = 10 units. Therefore,
Perimeter = 6 × 10
Therefore, the given regular hexagon perimeter = 60 units.
FAQs on Hexagon
What is a Hexagon?
A hexagon is a two-dimensional flat shape that has six angles, six edges, and six vertices. A hexagon can have equal or unequal sides and interior angles. It is a 6-sided polygon with two types - regular hexagon and irregular hexagon.
Are all 6-sided Shapes Hexagons?
A hexagon is a two-dimensional shape having 6 sides. It may be equal or unequal. Therefore, all six-sided closed shapes are hexagons.
What are the Three Attributes of a Hexagon?
The three attributes of a hexagon are:
- It has 6 sides
- It has 6 angles
- It has 6 corners
Does a Hexagon Always Have Equal Sides?
Hexagon may not necessarily have all sides equal. It can have sides of variable lengths too. The hexagon having equal sides is called a regular hexagon and the one with different sides is called an irregular hexagon.
How are Hexagons Classified?
A hexagon is classified based on the side lengths and angles. Based on this, hexagons are classified into regular (equal side-lengths and angles) and irregular (unequal side-lengths and angles) hexagons. Convex hexagons are the ones in which all the interior angles are less than 180° and concave hexagons are the ones in which at least one of the interior angles is greater than 180°.
What is the Sum of Interior Angles of a Hexagon?
In a hexagon, the sum of all 6 interior angles is always 720º. The sum of interior angles of a polygon is calculated using the formula, (n-2) × 180°, where 'n' is the number of sides of the polygon. Since a hexagon has 6 sides, taking 'n' as 6 we get. (6-2) × 180° gives 720°.
What is the Value of an Angle in a Regular Hexagon?
The measure of an angle in a regular hexagon is 120°.
How Many Diagonals Can be Drawn in a Regular Hexagon?
The formula to calculate the number of diagonals of a polygon is n(n-3)/2, where 'n' is the number of sides of the polygon. A hexagon has 6 sides. therefore, the number of diagonals is 6(6-3)/2, which is equal to 9.
How Many Lines of Symmetry are there in a Regular Hexagon?
For all regular polygons, the number of lines of symmetry is equal to the number of sides. Thus, for a regular hexagon, there are six lines of symmetry.
What is the Formula to Calculate the Area of a Regular Hexagon?
The formula to calculate the regular hexagon area is 3√3a2/2 square units, where 'a' is the side length of the regular hexagon.
How to Calculate Area of a Hexagon?
We can determine the area of a hexagon by identifying the length of the side of the hexagon. To find the area of a hexagon we use the formula, A = (3√3 S2)/2. Always write the final answer of area in square units.
What is the Formula to Calculate the Perimeter of a Hexagon?
The formula to calculate the regular hexagon perimeter is 6a units, where 'a' is the side length of the hexagon. In the case of an irregular hexagon, we add the side lengths. Mathematically, it can be expressed as, Perimeter of Hexagon = (a + b+ c+ d + e + f) units.