A polygon having actually eight sides is known as one octagon. If every the sides of one octagon room equal and also angles room the very same then the octagon is called a continuous octagon. A regular octagon has actually a total variety 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 an octagon measures45 degrees and the sum of all 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 given below.
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What Is Octagon Formula?
The octagon formula is used to calculation the area, perimeter, and diagonals of one octagon. To discover the area, perimeter, and diagonals of an octagon we usage the adhering to octagon formulas.
Formulas because that Octagon:
To discover the area of one octagon we usage the adhering to formula: Area the 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 an octagon we use the complying with formula: variety of Diagonals = n(n - 3)/2 = 8(8 - 3)/2 = 20
where,s = side lengthn = number of sides
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Examples UsingOctagon Formula
Example 1: calculate the perimeter and also area of an octagon having actually a side equal to 4 units using the octagon formula.
To Find: Perimeter and 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 of the octagonare 32 units and also 77.25483 units2.
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Example 2:An octagonal board has actually a perimeter same to 24 cm. Uncover its area utilizing the octagon formula.
To Find:Area that the octagon.Given: Perimeter = 24 cm.The perimeter the octagon = 8s24 = 8 ss = 3 cm.Usingthe octagon formula because that area,Area of octagon = 2s2(1 + √2)= 2 × 32(1 + √2)= 43.45cm2