maths classes
2D Shapes2cosacosb Formula30-60-90 Formulas3D ShapesAbsolute Value FormulaAcute AngleAcute Angle triangleAdditionAlgebra FormulasAlgebra of MatricesAlgebraic EquationsAlgebraic ExpressionsAngle FormulaAnnulusAnova FormulaAnti-derivative FormulaAntiderivative FormulaApplication of DerivativesApplications of IntegrationArc Length FormulaArccot FormulaArctan FormulaArea Formula for QuadrilateralsArea FormulasArea Of A Sector Of A Circle FormulaArea Of An Octagon FormulaArea Of Isosceles TriangleArea Of ShapesArea Under the Curve FormulaArea of RectangleArea of Regular Polygon FormulaArea of TriangleArea of a Circle FormulaArea of a Pentagon FormulaArea of a Square FormulaArea of a Trapezoid FormulaArithmetic Mean FormulaArithmetic ProgressionsArithmetic Sequence Recursive FormulaArithmetic and Geometric ProgressionAscending OrderAssociative Property FormulaAsymptote FormulaAverage Deviation FormulaAverage Rate of Change FormulaAveragesAxioms Of ProbabilityAxis of Symmetry FormulaBasic Math FormulasBasics Of AlgebraBinary FormulaBinomial Probability FormulaBinomial Theorem FormulaBinomial distributionBodmas RuleBoolean AlgebraBusiness MathematicsCalculusCelsius FormulaCentral Angle of a Circle FormulaCentral Limit Theorem FormulaCentroid of a Trapezoid FormulaChain RuleChain Rule FormulaChange of Base FormulaChi Square FormulaCirclesCircumference FormulaCoefficient of Determination FormulaCoefficient of Variation FormulaCofactor FormulaComplete the square formulaComplex numbersCompound Interest FormulaConditional Probability FormulaConeConfidence Interval FormulaCongruence of TrianglesCorrelation Coefficient FormulaCos Double Angle FormulaCos Square theta FormulaCos Theta FormulaCosec Cot FormulaCosecant FormulaCosine FormulaCovariance FormulaCubeCurated Maths Resources for Teachers – EdulyteCylinderDecimalsDifferential calculusDiscover the world of MathsEllipseEquilateral triangleEuler’s formulaEven numbersExponentsFractionFraction to decimalGeometric sequenceHeptagonHyperbolaIntegersIntegrationIntegration by partsLinesLocusMatricesNatural numbersNumber lineOdd numbersParallelogramPercentage formulaPerimeterPolygonPolynomialsPrismProbabilityPyramidPythagoras theoremRoman NumeralsScalene triangleSetsShapes NamesSimple interest formulaSlope formulaSolid shapesSphereSquareStandard deviation formulaSubtractionSymmetryTimeTrianglesTrigonometry formulaTypes of anglesValue of PiVariance formulaVectorVolume formulasVolume of a coneVolume of sphere formulaWhole numbers

Area Of An Octagon Formula

Edulyte Maths Lessons

Learn Maths anytime, anywhere

Sign Up

Cracking the Octagon Area Code: Geometry and Practical Applications

Comprehensive Definition, Description, Examples & Rules 

Edulyte Maths Lessons

Learn Maths anytime, anywhere

Sign Up
What will you learn

Introduction to Octagon Area

Polygons with 8 sides are known as octagons. Octagons are used in a variety of real-life applications like geometry and design. In geometry. It comes in handy in calculating the space occupied by shapes with 8 sides and in design and artwork, it helps create octagonal shapes like windows, lenses, etc. 

Understanding the Octagon

An octagon is a polygon with a total number of sides of 8. Here are some unique properties of the 8-sided figure:

  • An octagon always has 8 sides in total.
  • An octagon always has 8 angles.
  • All the interior angles in an octagon sum up to 1080 degrees.
  • All the exterior angles in an octagon sum up to 360 degrees.
  • Every interior angle in a regular octagon measures 135 degrees.
  • Every exterior angle in a regular octagon measures 45 degrees.
  • There are no more than 20 diagonals in an octagon. 

The Octagon Area Formula

The Area of a regular octagon follows the given formula for an accurate computation: 

A= 2 * (1+2) * s^2

A: Octagon’s area

s: Measure of one of the sides of a regular octagon

Finding the Area of an Octagon

Here is a step-by-step strategy of how you can discern the area of a regular octagon, with the help of the area of an octagon formula given above: 

  • The Area of a regular octagon follows the given formula for an accurate computation: A= 2 * (1+2) * s^2 (A: Octagon’s area, and s: Measure of one of the sides of a regular octagon)
  • Use the values available to you and place them in the equation of the formula
  • Carry out calculations and mathematical functions to get the final answer

Example: What will be the area of a regular octagon which has a side measuring up to 8 cm?

Solution: A= 2 * (1+2) * s^2 

A= 2 * 2.41 * 8^2

A= 4.82 * 64

A= 308.48 cm^2

Special Cases: Finding Area Without Height

Suppose you do not know the height of a trapezoid or an octagon, you can still know the area using other methods like

  • If you know the length of the base of the trapezoid or octagon and that of the non-parallel side, you can use the formula ½(b1+b2)s to calculate the area of the octagon where b1 and b2 are the lengths of the two bases and s is the length of the non-parallel side.
  • If you know the length of the base of the trapezoid or octagon and that of the diagonals, you can use the formula ½(b1+b2)d to calculate the area of the octagon where b1 and b2 are the lengths of the two bases and d is the average of the two diagonals of the octagon.

Real-World Applications

The knowledge of octagons is used in a variety of real-world applications, for example:

  • In architecture, octagons are used to create various items of everyday use like octagonal windows, lenses, etc. 
  • In construction, octagons are used to design roads and highways and do concrete work. 
  • In geometry, too, octagons have various uses as we can know how much space an 8-sided shape covers or its boundary length if we know octagons. 

Infographics: Visual Representation

Here is a visual representation of a trapezoid or octagon to help you better understand the octagon area formula: 

octagon area formula

Trapezoid Area vs. Other Shapes

Different formulas are used to compute the areas of different geometrical shapes. Here is a representation of the different kinds of shapes found commonly and their respective formulas for computing their area:

Trapezoid

The area of a trapezoid or an octagon can be computed with the formula:

A= 2 * (1+2) * s^2 (A: Area of octagon, s: length of the side of the octagon)

Rectangles

The area of rectangles is computed with the help of the formula: 

A= l * b, 

‘A’: area of the rectangle.

‘l’: length of one of the sides of the rectangle.

‘b’ refers to the breadth of one of the sides of the rectangle.

Parallelograms

A parallelogram’s area can be determined using the formula: 

A= b * h

 ‘A’: the area of the rectangle.

‘h’ is used to denote the height of the parallelogram.

‘b’ refers to the measure of the base of the parallelogram.

Common Mistakes and Pitfalls

Here is a list of some common errors when computing the area of octagons and what you should do to avoid them:

  • Often, people read the measurements given incorrectly. Make sure to double-check the measures available to you before starting your calculations.
  • People also make the mistake of using miscellaneous units throughout the formula, resulting in an inaccurate result. Ensure to maintain a unity of units in the formula for the most accurate and precise solutions. 
  • People often confuse the area formula for octagons with other geometrical shapes. Memorize the particular area formulas for each geometrical shape to carry out your calculations quickly and fool-proof. 

Step Up Your Math Game Today!

Free sign-up for a personalised dashboard, learning tools, and unlimited possibilities!

learn maths with edulyte

Key Takeaways

  1. An octagon is a polygon with a total number of sides of 8.

  2. The formula for computing the area of a regular octagon is given as: A= 2 * (1+2) * s^2 (A: Area of octagon, s: length of the side of the octagon)

  3. Octagons are used in a variety of fields like architecture, geometry, construction, and more.

Quiz

Check your score in the end

Quiz

Check your score in the end
Question of

Question comes here

Frequently Asked Questions

For times when you don’t know the measure of a side of a trapezoid or an octagon, you can still calculate the octagon area by taking the measure of the total distance from the central point of the octagon to the central point of any side (also called the apothem), and then multiply it with a half and the perimeter of the octagon (sum of the length of all sides). 

A= ½ * apothem * perimeter

In architecture and design, octagons create windows, roofs, lenses, etc. 

The area of an octagon is represented as 2 * (1+√2) * s^2, which multiplies the square of the length of the side with (1+√2) and then with 2. The area of a triangle is represented as ½*b*h, which takes the base and the height of the triangle into consideration, and that of a hexagon is represented as 3√3/2*s^2, which multiplies the square of the length of the side with the half of 3√3.

Yes, octagons have various unique properties that influence their area calculations, like:

  • There are always eight sides to an octagon.
  • There are always eight angles in an octagon.
  • An octagon’s internal angles cannot be greater than 1080 degrees in total.
  • In an octagon, the sum of all external angles cannot exceed 360 degrees.
  • In a standard octagon, each inner angle is 135 degrees.
  • In a standard octagon, each outer angle is 45 degrees.
  • An octagon can have no more than 20 diagonals. 

Using the incorrect formula and using inconsistent units are two typical errors to prevent when computing the area of an octagon. To prevent misunderstanding, remember the multiple area calculations for different geometric forms and utilise the same units of measurement throughout the formula.

Like
Share it with your friends

Learn Maths

2D Shapes2cosacosb Formula30-60-90 Formulas3D ShapesAbsolute Value FormulaAcute AngleAcute Angle triangleAdditionAlgebra FormulasAlgebra of MatricesAlgebraic EquationsAlgebraic ExpressionsAngle FormulaAnnulusAnova FormulaAnti-derivative FormulaAntiderivative FormulaApplication of DerivativesApplications of IntegrationArc Length FormulaArccot FormulaArctan FormulaArea Formula for QuadrilateralsArea FormulasArea Of A Sector Of A Circle FormulaArea Of An Octagon FormulaArea Of Isosceles TriangleArea Of ShapesArea Under the Curve FormulaArea of RectangleArea of Regular Polygon FormulaArea of TriangleArea of a Circle FormulaArea of a Pentagon FormulaArea of a Square FormulaArea of a Trapezoid FormulaArithmetic Mean FormulaArithmetic ProgressionsArithmetic Sequence Recursive FormulaArithmetic and Geometric ProgressionAscending OrderAssociative Property FormulaAsymptote FormulaAverage Deviation FormulaAverage Rate of Change FormulaAveragesAxioms Of ProbabilityAxis of Symmetry FormulaBasic Math FormulasBasics Of AlgebraBinary FormulaBinomial Probability FormulaBinomial Theorem FormulaBinomial distributionBodmas RuleBoolean AlgebraBusiness MathematicsCalculusCelsius FormulaCentral Angle of a Circle FormulaCentral Limit Theorem FormulaCentroid of a Trapezoid FormulaChain RuleChain Rule FormulaChange of Base FormulaChi Square FormulaCirclesCircumference FormulaCoefficient of Determination FormulaCoefficient of Variation FormulaCofactor FormulaComplete the square formulaComplex numbersCompound Interest FormulaConditional Probability FormulaConeConfidence Interval FormulaCongruence of TrianglesCorrelation Coefficient FormulaCos Double Angle FormulaCos Square theta FormulaCos Theta FormulaCosec Cot FormulaCosecant FormulaCosine FormulaCovariance FormulaCubeCurated Maths Resources for Teachers – EdulyteCylinderDecimalsDifferential calculusDiscover the world of MathsEllipseEquilateral triangleEuler’s formulaEven numbersExponentsFractionFraction to decimalGeometric sequenceHeptagonHyperbolaIntegersIntegrationIntegration by partsLinesLocusMatricesNatural numbersNumber lineOdd numbersParallelogramPercentage formulaPerimeterPolygonPolynomialsPrismProbabilityPyramidPythagoras theoremRoman NumeralsScalene triangleSetsShapes NamesSimple interest formulaSlope formulaSolid shapesSphereSquareStandard deviation formulaSubtractionSymmetryTimeTrianglesTrigonometry formulaTypes of anglesValue of PiVariance formulaVectorVolume formulasVolume of a coneVolume of sphere formulaWhole numbers
Newsletters

Sign up for Learner Newsletter

Subscribe now for discounts, learning resources, blogs and guides. We do not spam.

We won’t pass your details on to anyone else. By clicking the subscribe button you agree to our Terms of Use and Privacy Policy.

Newsletters

Sign up for Tutor Newsletter

Subscribe now for discounts, learning resources, blogs and guides. We do not spam.

We won’t pass your details on to anyone else. By clicking the subscribe button you agree to our Terms of Use and Privacy Policy.

PTE Tutorials: Customised Packages for Every Learner

Standard

$75 AUD

One time

popular

Premium

$275 AUD

One time

Elite

$575 AUD

One time