A polygon having eight sides is well-known as an octagon. If all the political parties of one octagon room equal and angles space the exact same then the octagon is dubbed a continual octagon. A regular octagon has actually a total number of 20 diagonals. The sum of all inner angles that a continuous octagon is 1080 degrees. Also, each interior angle is 135 degrees. Theexterior edge of an octagon measures45 degrees and the amount of every exterior angles is 360 degrees. Theoctagon formula is provided to calculation its area, perimeter of an octagon. Learn around the octagon formula with few examples given below.

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What Is Octagon Formula?

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

Formulas because that Octagon:

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

To uncover the perimeter of an octagon we usage the following formula: Perimeter of octagon= 8s

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

where,

s = next lengthn = variety of sides

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Examples UsingOctagon Formula

Example 1: calculation the perimeter and also area of an octagon having actually a side same to 4 devices using the octagon formula.

Solution:

To Find: Perimeter and 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 of the octagonare 32 units and also 77.25483 units2.

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

Solution:

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