Area of Regular Polygons
A regular polygon is a polygon that has equal sides and equal angles. Thus, the technique to calculate the value of the area of regular polygons is based on the formulas associated with each polygon. Let us have a look at the formulas of some commonly used regular polygons. The table added below shows Regular Polygon and the formulas for calculating their areas.
|
Regular Polygon |
Area Formula |
|---|---|
| Area of Equilateral Triangle | √3(side)2/4 |
| Area of Square | side × side |
| Area of Regular Pentagon | (5/2) (side) × (apothem) |
Now we see that the formula for area is different for different types of polygons. Suppose we have to give a common formula to find the area of the regular polygon. Then the formula for the same is,
A polygon having equal sides and equal angles is a regular polygon.
Area of Regular Polygon = (½) × Perimeter × Apothem
Area of Regular Polygon = (½) × (Number of Sides) × (Length of One Side) × (Apothem)
The use of this formula is explained in the example added below,
Example: Find the area of the regular polygon if the perimeter of the polygon is 20 cm and Apothem is 5 cm.
Solution:
Given,
- Perimeter of Polygon = 20 cm
- Length of Apothem = 5 cm
Area of Regular Polygon(A) = (½) × Perimeter × Apothem
A = (½) × 20 cm × 5 cm
A = 50 cm2
Thus, the area of the regular polygon is 50 cm2
Area of Polygons
Area of the Polygon is the area enclosed by the boundary of the polygon. A polygon is a closed, two-dimensional shape with straight sides. Each side of a polygon is a line segment, and the points where the sides meet are called vertices.
Area of Polygons
A polygon is a figure formed by joining ‘n’ straight lines such that it forms a closed figure. It has n-sides and there are different types of polygon, such as triangle, square, pentagon, etc. The area of the polygon is found by various methods and different types of polygons have different formulas to calculate its area. For example, suppose we have to find the area of a square (4-sided polygon) then its area is found by the formula, (side)2. Similarly, the area of other polygons is found.
Let’s learn more about Area of Polygons with formula, derivation and examples in detail below.
Table of Content
- Area of Polygon Definition
- Types of Polygon
- Regular Polygon
- Irregular Polygon
- Area of Polygon Formula
- Area of Regular Polygons
- Area of Irregular Polygon
- Area of Polygons with Coordinates
- Difference Between Perimeter and Area of Polygons
- Area of Polygon Examples
- Practice Questions on Area of Polygons
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