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130 LearnersLast updated on September 2, 2025
Area Of Regular Polygon Calculator
Calculators are reliable tools for solving simple mathematical problems and advanced calculations like trigonometry. Whether you’re cooking, tracking BMI, or planning a construction project, calculators will make your life easy. In this topic, we are going to talk about the area of regular polygon calculators.
What is an Area Of Regular Polygon Calculator?
An area of regular polygon calculator is a tool to find the area of regular polygons such as equilateral triangles, squares, and regular hexagons. Since regular polygons have equal sides and angles, the calculator helps compute the area using specific formulas. This calculator makes the computation much easier and faster, saving time and effort.
How to Use the Area Of Regular Polygon Calculator?
Given below is a step-by-step process on how to use the calculator:
Step 1: Enter the number of sides and the length of one side: Input these values into the given fields.
Step 2: Click on calculate: Click on the calculate button to compute the area and get the result.
Step 3: View the result: The calculator will display the result instantly.
How to Calculate the Area Of a Regular Polygon?
To calculate the area of a regular polygon, there is a simple formula that the calculator uses.
The formula involves the number of sides (n) and the length of one side (s).
Area = (n × s²) / (4 × tan(π/n))
This formula is derived from dividing the polygon into congruent isosceles triangles and calculating the area of those triangles.
Tips and Tricks for Using the Area Of Regular Polygon Calculator
When you use an area of regular polygon calculator, there are a few tips and tricks that can help you avoid mistakes:
Understand the formula and its derivation; this helps in understanding how the calculation works.
Remember that all sides and angles in a regular polygon are equal, which simplifies the process.
Ensure that the input values are in the same units to avoid errors in calculation.
Common Mistakes and How to Avoid Them When Using the Area Of Regular Polygon Calculator
We may think that when using a calculator, mistakes will not happen. But it is possible for users to make errors when using a calculator.
Mistake 1
Incorrect Input of Side Lengths or Number of Sides
Make sure the side lengths and the number of sides are input correctly.
For example, entering 6 sides for a hexagon instead of 5 for a pentagon can lead to incorrect results.
Mistake 2
Confusion Between Regular and Irregular Polygons
Ensure you are calculating the area of a regular polygon, where all sides and angles are equal. This formula does not apply to irregular polygons.
Mistake 3
Rounding Errors Before Completing the Calculation
Avoid rounding intermediate results too early.
For example, calculating the tangent value and rounding it prematurely can lead to inaccurate final results.
Mistake 4
Misinterpretation of Units
Ensure all measurements are in the same units (e.g., all in meters or all in feet) to avoid incorrect area calculations.
Mistake 5
Assuming the Formula Applies to All Polygons
This formula is specific to regular polygons only. Using it for irregular polygons will yield incorrect results.
Area Of Regular Polygon Calculator Examples
Problem 1
What is the area of a regular pentagon with side length 7 cm?
Use the formula:
Area = (n × s²) / (4 × tan(π/n))
For a pentagon (n = 5), with side length s = 7 cm:
Area = (5 × 7²) / (4 × tan(π/5)) ≈ 84.3 cm²
Explanation
By inputting the side length and number of sides into the formula, we calculate the area of the pentagon to be approximately 84.3 cm².
Problem 2
Find the area of a regular hexagon with a side length of 10 meters.
Use the formula:
Area = (n × s²) / (4 × tan(π/n))
For a hexagon (n = 6), with side length s = 10 m:
Area = (6 × 10²) / (4 × tan(π/6)) ≈ 259.8 m²
Explanation
The formula calculates the area of a hexagon with a side length of 10 meters to be approximately 259.8 m².
Problem 3
A regular octagon has sides of 4 inches each. What is the area?
Use the formula:
Area = (n × s²) / (4 × tan(π/n))
For an octagon (n = 8), with side length s = 4 in:
Area = (8 × 4²) / (4 × tan(π/8)) ≈ 77.3 in²
Explanation
The calculation shows that the area of the octagon is approximately 77.3 in².
Problem 4
Calculate the area of a regular decagon with side length 5 feet.
Use the formula:
Area = (n × s²) / (4 × tan(π/n))
For a decagon (n = 10), with side length s = 5 ft:
Area = (10 × 5²) / (4 × tan(π/10)) ≈ 192.4 ft²
Explanation
The area of the decagon is calculated to be approximately 192.4 ft² using the formula.
Problem 5
What is the area of a regular heptagon with each side measuring 9 meters?
Use the formula: Area = (n × s²) / (4 × tan(π/n)) For a heptagon (n = 7), with side length s = 9 m: Area = (7 × 9²) / (4 × tan(π/7)) ≈ 292.6 m²
Explanation
By applying the formula, the area of the heptagon is found to be approximately 292.6 m².
FAQs on Using the Area Of Regular Polygon Calculator
1.How do you calculate the area of a regular polygon?
2.Is the formula applicable to irregular polygons?
3.Why is the tangent function used in the formula?
4.How do I ensure accuracy when using the calculator?
5.Is the area of a regular polygon always a whole number?
Glossary of Terms for the Area Of Regular Polygon Calculator
- Regular Polygon: A polygon with all sides and angles equal.
- Tangent Function: A trigonometric function used to relate angles to side lengths in triangles.
- Isosceles Triangle: A triangle with two equal sides, often used in area calculations for polygons.
- Unit Consistency: Ensuring all measurements are in the same units to avoid calculation errors.
- Approximation: An estimated value derived from calculations, often involving decimal places.
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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
