Enter the side length or the apothem into the calculator to determine the area of an octagon.

Octagon Area Calculation Formula

The following formula is used to calculate the area of a regular octagon:

Area = 2 * (1 + √2) * sideLength²

Alternatively, if you know the apothem (a) and the side length (s), you can use:

Area = (perimeter * apothem) / 2

Variables:

  • Area is the total area of the octagon (square units)
  • sideLength is the length of one side of the octagon (units)
  • perimeter is the total length around the octagon (units)
  • apothem is the distance from the center to the midpoint of a side (units)

To calculate the area, multiply the appropriate values as given in the formula above.

What is Octagon Area Calculation?

Octagon area calculation refers to the process of determining the space enclosed within the eight sides of an octagon. This involves understanding the properties of the shape, such as the length of its sides or the apothem, and applying the correct formula to find the area. Accurate area calculation is important in various applications such as architecture, land surveying, and design.

How to Calculate Octagon Area?

The following steps outline how to calculate the area of an octagon using the given formula:

  1. First, determine your side length or the apothem of the octagon.
  2. If using side length, apply the formula: Area = 2 * (1 + √2) * sideLength².
  3. If using the apothem and side length, calculate the perimeter by multiplying the side length by 8.
  4. Use the formula: Area = (perimeter * apothem) / 2.
  5. Finally, calculate the area by plugging in the values.
  6. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem:

Use the following variables as an example problem to test your knowledge:

Side Length = 5 units

Apothem = 6.88 units

FAQ

1. What is an apothem?

An apothem is a line from the center of a regular polygon perpendicular to one of its sides. It is used in calculating the area of polygons.

2. How is the octagon area different from the perimeter?

The area measures the total space enclosed within the octagon, while the perimeter measures the total length around the octagon.

3. How often should I use the octagon area calculator?

It’s helpful to use the octagon area calculator whenever you need to determine the area for practical applications or when verifying geometric problems.

4. Can this calculator be used for irregular octagons?

No, this calculator is designed for regular octagons where all sides and angles are equal.

5. Is the calculator accurate?

The calculator provides an estimate of the area based on the inputs provided. For exact figures, it’s best to perform manual calculations and verify with multiple sources.