A polygon having actually eight political parties is known as one octagon. If every the sides of an octagon space equal and also angles room the very same then the octagon is called a constant octagon. A regular octagon has a total number of 20 diagonals. The sum of all interior angles of a consistent octagon is 1080 degrees. Also, each internal angle is 135 degrees. Theexterior angle of one octagon measures45 degrees and the amount of every exterior angle is 360 degrees. Theoctagon formula is provided to calculation its area, perimeter of one octagon. Learn about the octagon formula with couple of examples provided below.
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What Is Octagon Formula?
The octagon formula is used to calculate the area, perimeter, and also diagonals of an octagon. To find the area, perimeter, and diagonals of an octagon we usage the complying with octagon formulas.
Formulas because that Octagon:
To uncover the area of an octagon we usage the complying with formula: Area of octagon formula=2× s2× (1 + √2)
To uncover the perimeter of one octagon we usage the complying with formula: Perimeter that octagon= 8s
To discover the number of diagonals of one octagon we use the following formula: variety of Diagonals = n(n - 3)/2 = 8(8 - 3)/2 = 20
where,s = side lengthn = variety of sides
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Examples UsingOctagon Formula
Example 1: calculation the perimeter and area of an octagon having actually a side equal to 4 units using the octagon formula.
To Find: Perimeter and also AreaGiven:s= 4 units.Using the octagon formula for perimeterPerimeter(P) = 8sP = 8 × 4P = 32 unitsUsingthe octagon formula for areaArea that octagon= 2s2(1 + √2)= 2 × 42(1 + √2)= 77.25483 units2
Answer: Perimeter and also area the the octagonare 32 units and 77.25483 units2.
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Example 2:An octagonal board has a perimeter same to 24 cm. Discover its area making use of the octagon formula.
To Find:Area that the octagon.Given: Perimeter = 24 cm.The perimeter that octagon = 8s24 = 8 ss = 3 cm.Usingthe octagon formula for area,Area that octagon = 2s2(1 + √2)= 2 × 32(1 + √2)= 43.45cm2