Area of Polygons with Coordinates
If the coordinates of any polygon are given then its area is calculated using the steps discussed below.
Step 1: First find the distance of all the sides of the polygon, using the distance formula as,
D = √{(x2 – x1)2 + (y2 – y1)2}
Step 2: Finding all the sides of the polygon we first check whether the polygon is a regular polygon or not.
Step 3: Now, if the polygon is a regular polygon then use the formula,
Area of Regular Polygon = (Number of Sides × Length of One Side × Apothem)/2
Step 4: If the polygon is an irregular polygon then its area is calculated by dividing the polygon into smaller polygons then the area of the smaller polygon is found using the known formula. And then the sum is found which gives the area of the irregular polygon.
Example: Find the area of the polygon with coordinates A(1, 1), B(4, 1), C(1, 3), and D(4, 3)
Solution:
AB = √{(3)2 + (0)2} = 3
BC = √{(3)2 + (2)2} = √13
CD = √{(3)2 + (0)2} = 3
DA = √{(3)2 + (2)2} = √13
Here we see that AB = BC and CD = DA. Hence, ABCD is a rectangle
Therefore Area of Rectangle ABCD is 3√13
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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