Introduction to Regular Polygon Area Calculation
In geometry, a regular polygon is a shape with equal sides and equal angles. Calculating the area of a regular polygon can be a bit more complex than calculating the area of a rectangle or triangle, but with the right formula and tools, it can be done easily. In this post, we will discuss the formula for calculating the area of a regular polygon and provide a worksheet and calculator to help you practice.
Formula for Regular Polygon Area Calculation
The formula for calculating the area of a regular polygon is:
A = (n × s^2) / (4 × tan(π/n))
Where:
- A is the area of the polygon
- n is the number of sides of the polygon
- s is the length of one side of the polygon
- tan is the tangent function
- π is a mathematical constant approximately equal to 3.14
How to Use the Formula
To use the formula, simply plug in the values for n and s, and calculate the result. For example, let’s say we want to calculate the area of a regular hexagon (6-sided polygon) with sides of length 5 units.
A = (6 × 5^2) / (4 × tan(π/6)) A = (6 × 25) / (4 × 0.577) A = 150 / 2.308 A = 65.03 square units
Regular Polygon Area Worksheet
Here is a worksheet with some practice problems to help you get started:
| Polygon | Number of Sides (n) | Side Length (s) | Area (A) |
|---|---|---|---|
| Triangle | 3 | 4 | ? |
| Square | 4 | 6 | ? |
| Pentagon | 5 | 8 | ? |
| Hexagon | 6 | 10 | ? |
| Heptagon | 7 | 12 | ? |
Try to calculate the area of each polygon using the formula above.
Regular Polygon Area Calculator
If you want to calculate the area of a regular polygon quickly and easily, you can use our online calculator:
| Number of Sides (n) | Side Length (s) | Area (A) |
|---|---|---|
Simply enter the number of sides and side length, and the calculator will compute the area for you.
🤔 Note: This calculator assumes that the input values are valid and does not perform any error checking.
By using the formula and calculator provided, you should be able to calculate the area of any regular polygon with ease.
In summary, calculating the area of a regular polygon involves using the formula A = (n × s^2) / (4 × tan(π/n)), where n is the number of sides and s is the length of one side. With practice and the help of our worksheet and calculator, you can become proficient in calculating the area of regular polygons.
What is a regular polygon?
+A regular polygon is a shape with equal sides and equal angles.
How do I calculate the area of a regular polygon?
+Use the formula A = (n × s^2) / (4 × tan(π/n)), where n is the number of sides and s is the length of one side.
What is the difference between a regular polygon and an irregular polygon?
+A regular polygon has equal sides and equal angles, while an irregular polygon does not.
