Area Of Octagon Calculator
2026-02-28 10:51 Diff
https://brightchamps.com/en-us/math/calculators/area-of-octagon-calculator

204 Learners

Last updated on August 5, 2025

A calculator is a tool designed to perform both basic arithmetic operations and advanced calculations, such as those involving geometry. It is especially helpful for completing mathematical school projects or exploring complex mathematical concepts. In this topic, we will discuss the Area Of Octagon Calculator.

What is the Area Of Octagon Calculator

The Area Of Octagon Calculator is a tool designed for calculating the area of an octagon.

An octagon is a two-dimensional shape with eight sides.

Each side of a regular octagon is equal in length, and all interior angles are equal.

The term "octagon" comes from the Greek word "okta," meaning "eight," and "gonia," meaning "angle."

How to Use the Area Of Octagon Calculator

For calculating the area of an octagon using the calculator, we need to follow the steps below -

Step 1: Input: Enter the side length

Step 2: Click: Calculate Area. By doing so, the side length we have given as input will be processed

Step 3: You will see the area of the octagon in the output column

Explore Our Programs

Tips and Tricks for Using the Area Of Octagon Calculator

Mentioned below are some tips to help you get the right answer using the Area Of Octagon Calculator.

Know the formula: The formula for the area of a regular octagon is (2(1+√{2})s2), where ‘s’ is the side length.

Use the Right Units: Make sure the side length is in the right units, like centimeters or meters.

The answer will be in square units (like square centimeters or square meters), so it’s important to match them.

Enter Correct Numbers: When entering the side length, make sure the numbers are accurate.

Small mistakes can lead to big differences, especially with larger numbers.

Common Mistakes and How to Avoid Them When Using the Area Of Octagon Calculator

Calculators mostly help us with quick solutions.

For calculating complex math questions, students must know the intricate features of a calculator.

Given below are some common mistakes and solutions to tackle these mistakes.

Problem 1

Help Emma find the area of a regular octagonal garden if each side is 7 m.

Okay, lets begin

We find the area of the garden to be approximately 169.71 m²

Explanation

To find the area, we use the formula: Area = \(2(1+\√{2})s2\)

Here, the value of ‘s’ is given as 7

Now, we substitute the value of ‘s’ in the formula: Area = \(2(1+\√{2}) \times (7)2\) ≈ 169.71 m²

Well explained 👍

Problem 2

The side length ‘s’ of a stop sign is 9 cm. What will be its area?

Okay, lets begin

The area is approximately 392.52 cm²

Explanation

To find the area, we use the formula: Area = \(2(1+\√{2})s2\)

Since the side length is given as 9, we can find the area as Area = \(2(1+\√{2}) \times (9)2\) ≈ 392.52 cm²

Well explained 👍

Problem 3

Find the area of a square with side length ‘s’ as 8 cm and the area of an octagon with side length 4 cm. After finding the area of the square and octagon, take their sum.

Okay, lets begin

We will get the sum as approximately 148.96 cm²

Explanation

For the area of a square, we use the formula ‘A = s2’, and for the octagon, we use ‘A = 2(1+\√{2})s2’.

Area of square = \(s2 = 82 = 64\) cm²

Area of octagon = \(2(1+\√{2}) \times (4)2\) ≈ 84.96 cm²

The sum of areas = area of square + area of octagon = 64 + 84.96 ≈ 148.96 cm²

Well explained 👍

Problem 4

The side length of a decorative octagonal mirror is 12 cm. Find its area.

Okay, lets begin

We find the area of the decorative octagonal mirror to be approximately 695.69 cm²

Explanation

Area = \(2(1+\√{2})s2\) = \(2(1+\√{2}) \times (12)2\) ≈ 695.69 cm²

Well explained 👍

Problem 5

Olivia wants to design an octagonal table top. If the side length of the table top is 15 cm, help Olivia find its area.

Okay, lets begin

The area of the octagonal table top is approximately 1308.29 cm²

Explanation

Area of octagonal table top = \(2(1+\√{2})s2\) = \(2(1+√{2}) \times (15)2\) ≈ 1308.29 cm²

Well explained 👍

FAQs on Using the Area Of Octagon Calculator

1.What is the area of the octagon?

The area of the octagon uses the formula \(2(1+\√{2})s2\), where ‘s’ is the side length.

2.What is the value of ‘s’ that gets entered as ‘0’?

The side length should always be a positive number.

If we enter ‘0’ as the side length, then the calculator will show the result as invalid.

The length of the side can’t be 0.

3.What will be the area of the octagon if the side length is given as 5?

Applying the value of the side length as 5 in the formula, we get the area of the octagon as approximately 120.71 cm².

4.What units are used to represent the area?

For representing the area, the units mostly used are square meters (m²) and square centimeters (cm²).

5.Can we use this calculator to find the area of an irregular octagon?

No, this calculator is specifically for regular octagons with equal sides and angles.

The area of an irregular octagon requires different methods.

Important Glossary for the Area Of Octagon Calculator

  • Area: It is the amount of space occupied by a two-dimensional shape.

                     It is measured in square meters (m²) or square centimeters (cm²).

  • Side Length: The length of one side of a polygon. For example, in \(2(1+\√{2}) \times 72\), ‘7’ is the side length.
  • Regular Octagon: An eight-sided polygon with equal side lengths and equal interior angles.
  • Square Units: Units used to measure area, such as m² and cm².
  • Pi (π): A mathematical constant representing the ratio of a circle's circumference to its diameter, approximately 3.14159, but not used in the octagon area formula.

Seyed Ali Fathima S

About the Author

Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.

Fun Fact

: She has songs for each table which helps her to remember the tables