A polygon having actually eight sides is recognized as an octagon. If every the political parties of one octagon space equal and also angles space the same then the octagon is dubbed a regular octagon. A continuous octagon has a total number of 20 diagonals. The sum of all internal angles the a regular octagon is 1080 degrees. Also, each inner angle is 135 degrees. Theexterior edge of one octagon measures45 degrees and the amount of every exterior angles is 360 degrees. Theoctagon formula is used to calculation its area, perimeter of one octagon. Learn about the octagon formula with couple of examples offered below.

You are watching: What is the exterior angle of a regular octagon

## What Is Octagon Formula?

The octagon formula is provided to calculation the area, perimeter, and diagonals of an octagon. To find the area, perimeter, and diagonals of an octagon we usage the adhering to octagon formulas.

### Formulas because that Octagon:

To uncover the area of an octagon we use the following formula: Area of octagon formula=2× s2× (1 + √2)

To uncover the perimeter of an octagon we use the adhering to formula: Perimeter the octagon= 8s

To uncover the variety of diagonals of one octagon we use the following formula: number of Diagonals = n(n - 3)/2 = 8(8 - 3)/2 = 20

where,

s = next lengthn = number of sidesHave concerns on simple mathematical concepts?

Become a problem-solving champ making use of logic, not rules. Learn the why behind math v our certified experts

Book a complimentary Trial Class

## Examples UsingOctagon Formula

**Example 1:** calculation the perimeter and also area of one octagon having a side same to 4 units using the octagon formula.

**Solution:**

To Find: Perimeter and also AreaGiven:s= 4 units.Using the octagon formula because that perimeterPerimeter(P) = 8sP = 8 × 4P = 32 unitsUsingthe octagon formula because that areaArea of octagon= 2s2(1 + √2)= 2 × 42(1 + √2)= 77.25483 units2

**Answer:** Perimeter and area the the octagonare 32 units and also 77.25483 units2.

See more: What Is A Trunk Lift Exercise ? Trunk Lifts

**Example 2:**An octagonal board has actually a perimeter equal to 24 cm. Uncover its area utilizing the octagon formula.

**Solution:**

To Find:Area of the octagon.Given: Perimeter = 24 cm.The perimeter the octagon = 8s24 = 8 ss = 3 cm.Usingthe octagon formula for area,Area the octagon = 2s2(1 + √2)= 2 × 32(1 + √2)= 43.45cm2