A polygon having six political parties is known as a hexagon.There are few types of hexagons i.e, continual hexagon, irregular hexagon, and,concave hexagon.If every the sides of a hexagon space equal and also angles space the same then the hexagon is dubbed a constant hexagon. Ahexagon has actually a total number of 9 diagonals. The amount of all internal angles of a constant hexagon is 720 degrees. Also, each interior angle is 120 degrees. A continuous hexagon has an exterior edge of60 degrees and the sum of every exterior angle is 360 degrees. The hexagon formula is provided to calculate its area and also perimeter.

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What Is Hexagon Formula?

The hexagon formula is defined as a collection of formulas to calculate the perimeter, area, and diagonals that the hexagon. The hexagon formulas apply directly to continual hexagons.

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Hexagon Formula

The hexagon formula have the right to be created as:

Area the hexagon:(dfrac(3sqrt3 ext s^2)2)

Where,

s = side length.

Perimeter of hexagon:6s

Where,

s = next length.

Diagonals the a hexagon: 2s and√3s

Where,

s = side length

Special Formula:Area = 1/2×perimeter×apothem

Let us see the applications of the hexagon formulain the following solved examples.

Derivation that Hexagon Formula

Consider a continual hexagon of side s. Then,

Area the a hexagon

Find the area of one of the triangles.Multiply by 6.

Thus,(dfrac(3sqrt3 ext s^2)2)

Perimeter of a hexagon

The perimeter of any type of polygon is the sum of every theside lengths.A constant hexagon has actually 6 sides. Thus, main point the side size by 6.

Thus, the formula because that the perimeter that a continual hexagon is offered as, P=6×a

Diagonal that a hexagon

In a hexagon, there are 6(6-3)/2 = 9diagonalsFor longerdiagonal, d= 2s, and for much shorter diagonal, d = √3s, whereby s refers to the next of the hexagon.

Thus, the formula for the diagonalof a hexagon is offered as, d = 2s, and√3s


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Solved instances Using Hexagon Formula

Example 1: calculation the perimeter and area that a consistent hexagon having actually a side equal to 4 units.

Solution:

To Find: Perimeter and also AreaGiven:s= 4 units.Using the hexagon formula because that perimeterPerimeter(P) = 6sP = (6 imes 4)P = 24 unitsUsingthe constant hexagon formula forArea( extArea of hexagon =dfrac(3sqrt3 ext s^2)2)= (dfrac(3sqrt3 imes 4^2)2)= 41.56 units2Answer: Perimeter and also area that the hexagon are 24 units and 41.56 units2.

Example 2:A hexagonal board has a perimeter equal to 12 inches. Uncover its area.

Solution:

To Find:Area the the hexagon.Given: Perimeter = 12 inches.The perimeter of hexagon = 6s12 = 6 ss = 2inches.Usingthe hexagon formula forArea,( extArea of hexagon =dfrac(3sqrt3 ext s^2)2)=(dfrac(3sqrt3 imes 2^2)2)=10.39 inches2

Answer: The areaof the hexagonal board is 10.39 inches2.

Example 3: recognize the side size of the continual hexagon whose perimeter is 24units.

Solution:

To Find:Side size of hexagonGiven:perimeter= 24units.Using the hexagon formula for perimeterPerimeter(P) = 6s24= (6 imes s)s = 24/6units= 4unitsAnswer:The side lengthof the hexagon is 4 units.


FAQs top top Hexagon Formula

What Is Hexagon Formula in Geometry?

The hexagon formula calculates the perimeter, area, and also diagonals of the hexagon. The hexagon formulas use directly to continuous hexagons. The hexagon formulas are provided as,Area the hexagon =(dfrac(3sqrt3 ext s^2)2)and Perimeter of hexagon =6s, whereby s = side length.

What Is s in Hexagon Formula?

In hexagon formulas, Area the hexagon=(dfrac(3sqrt3 ext s^2)2) andPerimeter the hexagon =6s, s refers to the next of the consistent hexagon.

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How To use Hexagon Formula?

To usage the hexagon formula for a provided hexagon

Step 1: determine if the offered hexagon is consistent or irregular.Step 2: determine the side of the continual hexagon.Step 3: placed the worth in the ideal formula,Area of hexagon =(dfrac(3sqrt3 ext s^2)2) andPerimeter of hexagon =6s

What Is Hexagon Formula because that Irregular Hexagon?

In the instance of an irregular hexagon, dividethe offered hexagon right into rectangles and also right triangles and also then uncover the area of each form whereasto calculation perimeter, just include the lengths of every its sides.