A polygon having eight political parties is recognized as one octagon. If all the political parties of an octagon are equal and angles space the very same then the octagon is dubbed a constant octagon. A continuous octagon has a total number of 20 diagonals. The amount of all internal angles of a consistent octagon is 1080 degrees. Also, each interior angle is 135 degrees. Theexterior angle of one octagon measures45 degrees and the amount of every exterior angles is 360 degrees. Theoctagon formula is provided to calculate its area, perimeter of one octagon. Learn around the octagon formula with couple of examples offered below.

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

*

What Is Octagon Formula?

The octagon formula is offered to calculate the area, perimeter, and also diagonals of one octagon. To uncover the area, perimeter, and also diagonals of one octagon we usage the adhering to octagon formulas.

Formulas for Octagon:

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

To find the perimeter of one octagon we use the adhering to formula: Perimeter of octagon= 8s

To uncover the variety of diagonals of an octagon we usage the complying with formula: number of Diagonals = n(n - 3)/2 = 8(8 - 3)/2 = 20

where,

s = next lengthn = variety of sides

*


Have questions on straightforward mathematical concepts?
Become a problem-solving champ using logic, no rules. Find out the why behind math v our certified experts

Book a cost-free Trial Class


Examples UsingOctagon Formula

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

Solution:

To Find: Perimeter and AreaGiven:s= 4 units.Using the octagon formula for 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 of the octagonare 32 units and also 77.25483 units2.

See more: Is It Possible To Do Work On An Object That Remains At Rest, Work Done By A Constant Force

Example 2:An octagonal board has actually a perimeter equal to 24 cm. Find 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 that octagon = 2s2(1 + √2)= 2 × 32(1 + √2)= 43.45cm2