Regular polygon area calculator
Area
Regular polygon
Regular polygon area
A regular polygon is a polygon with sides of equal length and angles of equal measure. The area of a regular polygon is the amount of space inside the polygon. Calculating the area of a regular polygon can be a challenging task, especially if the polygon has more than four sides. But don't worry, our regular polygon area calculator makes it easy for you. In this article, we'll discuss the formula for finding the area of a regular polygon and show you how to use our calculator.
Formula for Regular Polygon Area
The formula for the area of a regular polygon can be calculated using two methods:
- By using apothem and perimeter of the polygon, the formula for the area is:S = (1/2) * \text{apothem} * \text{perimeter} where S is the area of the polygon, apothem is the distance from the center of the polygon to the midpoint of a side, and perimeter is the distance around the polygon.
- By using the number of edges and the length of the edge, the formula for the area S = \dfrac{na^2}{4tg\left(\dfrac{360^o}{2n}\right)}where n is the number of edges and a is the length of the edge.
How to Use the Regular Polygon Area Calculator
Our regular polygon area calculator makes it easy to find the area of your regular polygon. To use the calculator:
- Enter the number of edges (n) of the polygon.
- Enter the length of the edge (a).
- Or, enter the apothem (a) and perimeter (p), respectively.
- The calculator will automatically calculate and show you the area of the regular polygon.
Regular Polygon Area Examples
Here are some examples of finding the area of a regular polygon using the formulas:
Example 1: Find the area of a regular hexagon with a side length of 8.
Using the formula S = \dfrac{6*8^2}{4tg\left(\dfrac{360^o}{2*6}\right)} = 166.27
Example 2: Find the area of a regular pentagon with a side length of 5 and apothem length of x.
Using the formula S = \dfrac{1}{2} * \text{apothem} * \text{perimeter}
Conclusion
Calculating the area of a regular polygon is an important skill in geometry. Our regular polygon area calculator and formula make it easy to find the area of your regular polygon. Try it out for yourself and see how easy it can be!
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