104 LearnersLast updated on August 5th, 2025
Area Of Octagon Calculator
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
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.
Mistake 1
Rounding off too soon
Rounding the decimal number too soon can lead to wrong results.
For example, if the area is 45.67 cm², don’t round it to 46 right away.
Finish the calculation first.
Mistake 2
Entering the wrong number as the side length
Make sure to double-check the number you are going to enter as the side length.
If you enter the side length as ‘5’ instead of 6, the result will be incorrect.
Mistake 3
Mixing up the area formula with the perimeter formula
The perimeter of an octagon is calculated as '8s', whereas the area uses '2(1+√{2})s2'.
Using the wrong formula will give the wrong result.
Mistake 4
Relying too much on the calculator
The calculator gives an estimate.
Real objects may not be perfect, so the answer might be slightly different.
Keep in mind that it's an approximation.
Mistake 5
Mixing up the positive and negative signs
Always check that you’ve entered the correct positive (+) or negative (–) signs.
A small mistake, like using the wrong sign for the side length, can completely change the result.
Make sure the signs are correct before finishing your calculation.
For example, if the side length is 10 cm, entering -10 cm instead of +10 cm could give you an incorrect area.
Area Of Octagon Calculator Examples
Problem 1
Help Emma find the area of a regular octagonal garden if each side is 7 m.
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
Problem 2
The side length ‘s’ of a stop sign is 9 cm. What will be its area?
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
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.
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
Problem 4
The side length of a decorative octagonal mirror is 12 cm. Find its area.
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
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.
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
FAQs on Using the Area Of Octagon Calculator
1.What is the area of the octagon?
2.What is the value of ‘s’ that gets entered as ‘0’?
3.What will be the area of the octagon if the side length is given as 5?
4.What units are used to represent the area?
5.Can we use this calculator to find the area of an irregular octagon?
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.
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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
