103 LearnersLast updated on June 24th, 2025
Regular Polygon 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 Regular Polygon Calculator.
What is the Regular Polygon Calculator
The Regular Polygon Calculator is a tool designed for calculating various properties of a regular polygon. A regular polygon is a two-dimensional shape with all sides and angles equal.
The word polygon comes from the Greek words "poly", meaning "many", and "gon", meaning "angle".
How to Use the Regular Polygon Calculator
For calculating the properties of a regular polygon, using the calculator, we need to follow the steps below -
Step 1: Input: Enter the number of sides and the length of one side
Step 2: Click: Calculate Properties. By doing so, the inputs we have given will get processed
Step 3: You will see the properties of the regular polygon, such as area and perimeter, in the output column
Tips and Tricks for Using the Regular Polygon Calculator
Mentioned below are some tips to help you get the right answer using the Regular Polygon Calculator.
Know the formula:
The formula for the perimeter of a regular polygon is ‘n × s’, where ‘n’ is the number of sides and ‘s’ is the length of one side. The area can be calculated using the formula ‘(n × s²) / (4 × tan(π/n))’.
Use the Right Units:
Make sure the side length is in the right units, like centimeters or meters. The answer will be in the corresponding units, such as square centimeters for area, so it’s important to match them.
Enter Correct Numbers:
When entering the number of sides and side length, make sure the numbers are accurate. Small mistakes can lead to big differences in the results.
Common Mistakes and How to Avoid Them When Using the Regular Polygon 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 15.67 cm², don’t round it to 16 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 ‘6’ instead of ‘7’, the result will be incorrect.
Mistake 3
Mixing up formulas for perimeter and area
The perimeter is calculated with ‘n × s’, whereas the area uses ‘(n × s²) / (4 × tan(π/n))’. 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 29 cm, entering -29 cm instead of +29 cm could give you an incorrect result.
Regular Polygon Calculator Examples
Problem 1
Help Sarah find the perimeter of a regular hexagon if each side is 9 cm.
We find the perimeter of the regular hexagon to be 54 cm.
Explanation
To find the perimeter, we use the formula: Perimeter = n × s
Here, the number of sides ‘n’ is 6, and the length of one side ‘s’ is 9
Now, we substitute the values in the formula: Perimeter = 6 × 9 = 54 cm
Problem 2
The side length of a regular pentagon is 12 cm. What will be its area?
The area is approximately 247.75 cm².
Explanation
To find the area, we use the formula: Area = (n × s²) / (4 × tan(π/n))
Since the number of sides ‘n’ is 5 and the side length ‘s’ is 12,
we can find the area as Area = (5 × 12²) / (4 × tan(π/5)) ≈ 247.75 cm²
Problem 3
Find the area of a regular triangle with side length ‘s’ as 6 cm and the perimeter of a regular octagon with side length 3 cm. After finding the area and perimeter, take their sum.
We will get the sum as approximately 36.92 cm².
Explanation
For the area of a regular triangle, we use the formula ‘Area = (n × s²) / (4 × tan(π/n))’,
and for the perimeter of an octagon, we use ‘Perimeter = n × s’.
Area of triangle = (3 × 6²) / (4 × tan(π/3)) ≈ 15.59 cm²
Perimeter of octagon = 8 × 3 = 24 cm
The sum = Area of triangle + Perimeter of octagon = 15.59 + 24 = 39.59 cm²
Problem 4
The side length of a regular heptagon is 15 cm. Find its perimeter.
We find the perimeter of the regular heptagon to be 105 cm.
Explanation
Perimeter = n × s = 7 × 15 = 105 cm
Problem 5
John wants to calculate the area of a regular decagon. If each side of the decagon is 30 cm, help John find its area.
The area of the regular decagon is approximately 2250 cm².
Explanation
Area of regular decagon = (n × s²) / (4 × tan(π/n))
= (10 × 30²) / (4 × tan(π/10)) ≈ 2250 cm²
FAQs on Using the Regular Polygon Calculator
1.What is the perimeter of a regular polygon?
2.What happens if the side length is entered as ‘0’?
3.What will be the area of a regular pentagon if each side is given as 3?
4.What units are used to represent the area and perimeter?
5.Can we use this calculator to find the properties of an irregular polygon?
Important Glossary for the Regular Polygon Calculator
- Regular Polygon: A polygon with all sides and angles equal.
- Perimeter: The total length around the boundary of a polygon.
- Area: The amount of space enclosed by a polygon, measured in square units.
- Side Length: The length of one of the equal sides of a regular polygon.
- Tangent (tan): A trigonometric function, used here to calculate the area of a regular polygon.
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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
