The Octagon Calculator is designed to help users compute various properties of a regular octagon—specifically its Perimeter, Side Length, and Area. Here’s an overview of the concepts behind these calculations and how the calculator works.
Octagon Calculator
Solve for Perimeter
Solve for Side
Solve for Area
Perimeter (P): 0 units
Side (a): 0 units
Area (A): 0 square units
Octagon Representation
Solve for Perimeter
Solve for Side
Solve for Area
Perimeter (P): 0 units
Side (a): 0 units
Area (A): 0 square units
Octagon Representation
Octagon Calculator
Understanding the Octagon
An octagon is a polygon with 8 equal sides and 8 equal angles. A regular octagon has:
- All sides equal in length.
- All internal angles equal to 135°.
Formulas Used in the Calculator
To calculate the properties of a regular octagon, we use the following formulas:
1. Perimeter
The perimeter of an octagon is the total length around it:
P = 8 × a
Where:
- P = Perimeter
- a = Side length
2. Side Length
If the perimeter is known, the side length can be calculated as:
a = P ÷ 8
Where:
- a = Side length
- P = Perimeter
3. Area
The area of a regular octagon is given by:
A = 2(1 + √2) × a²
Where:
- A = Area
- a = Side length
- √2 = Approximately 1.414
Visual Representation
Illustration of a regular octagon with 8 equal sides.
Understanding the Octagon
An octagon is a polygon with 8 equal sides and 8 equal angles. A regular octagon has:
- All sides equal in length.
- All internal angles equal to 135°.
Formulas Used in the Calculator
To calculate the properties of a regular octagon, we use the following formulas:
1. Perimeter
The perimeter of an octagon is the total length around it:
P = 8 × a
Where:
- P = Perimeter
- a = Side length
2. Side Length
If the perimeter is known, the side length can be calculated as:
a = P ÷ 8
Where:
- a = Side length
- P = Perimeter
3. Area
The area of a regular octagon is given by:
A = 2(1 + √2) × a²
Where:
- A = Area
- a = Side length
- √2 = Approximately 1.414
Visual Representation
Illustration of a regular octagon with 8 equal sides.