Perimeter of Hexagon Formula

Perimeter of Hexagon Formula

Generally speaking, a hexagon is a six-sided polygon. All simple hexagons (without self-intersecting faces) have 720° of internal angles. Hexagons that are both equilateral and equiangular are defined as regular hexagons. Despite having circumscribed circles, it is bicentric (it has an enveloping circle) and tangential (it has an encircling circle).

Properties

• In a regular hexagon, the sum of all interior angles is 720 degrees , while the sum of exterior angles is 360 degrees

• In a regular hexagon, the measurement of each interior angle is 120 degrees, and the measurement of each exterior angle is 60 degrees

• Typically, a hexagon can be divided into six triangles of equal length

• Regular hexagons have parallel opposite sides

All six sides of the rectangle are added up to define the perimeter

Formula: 6 × s

In this case, s denotes the hexagon’s side.

Derivation

There are six sides, each of which is equal. Let us call one side an ‘s’. Hence, the sum of six sides is s + s + s + s + s + s.

That means the perimeter is 6s.

Solved Example

Q1: Find the perimeter of the given regular hexagon whose side measure is 12 cm.

Ans: Let s be the side of a regular hexagon, then the perimeter of a regular hexagon

= 6s

Therefore, Perimeter of the regular hexagon with a 12 cm side = 6 x 12

= 72 cm

Q2: Evaluate the length of the side of a regular hexagon if its perimeter is given as 78 cm.

Ans: If s represents the side of a regular hexagon,

then the perimeter of a regular hexagon = 6s

According to the question,

6s = 78

Now, transposing 6 into RHS we have,

s = 78/6

So, s(side of the regular hexagon) = 13 cm

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