Example: What is the area of the polygon formed by the coordinates A 0,0 , B 0, 2 , C 2, 2 , and D 2, 0? It can be seen, the obtained figure shows a four-sided polygon.
In order to understand whether it is a regular polygon or not, we find the distance between all the points. Now that we know the length of all sides of the given polygon is the same, it shows, it is a square.
Hence, the area of the polygon with coordinates 0,0 , 0, 2 , 2, 2 , and 2, 0 is 4 square units. Solution: It can be seen that the given polygon is an irregular polygon. The area of polygon can be found by dividing the given polygon into a trapezium and a triangle where ABCE forms a trapezium while ECD forms a triangle.
In order to find the area of polygon let us first list the given values:. Example 2: Determine the length of the rectangle, i f the area of a rectangle is square units and the width breadth is 5 units. Thus, the length of the rectangle is calculated as:. The space enclosed by any polygon in a two-dimensional plane is defined as the area of the polygon. We write the unit of area of a polygon in square units where the unit can be SI units like meters or centimeters, etc.
The area of a polygon can be calculated by understanding whether the given polygon is a regular polygon or an irregular polygon. The steps to calculate the area of polygons are:. The perimeter of a polygon is the total length of its boundary, whereas, the area of a polygon is the region occupied by it.
The perimeter of a polygon is obtained by adding the length of all its sides while the area of a polygon is obtained by using the required formula depending upon whether the given polygon is a regular polygon or not.
The unit of the perimeter of a polygon is always given in linear units as it is one-dimensional while the unit of the area of a polygon is always given in square units because the area is a two-dimensional concept. Observe the following steps for the whole procedure:.
Substituting the value of the apothem and the perimeter, the area of the polygon can be calculated. Learn Practice Download. For example:. For example, you obtain the coordinates with MeshCoordinates[R]. In old versions e. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group.
Create a free Team What is Teams? Learn more. Asked 4 years ago. Active 4 years ago. Viewed times. Other options for getting a vertex list for the difference of two polygons are also welcome. Improve this question. Frobryo Frobryo 23 3 3 bronze badges. The center of a regular polygon is the point of intersection of the perpendicular bisectors of the sides. The segment from a vertex to the center is the radius.
The perpendicular segment from the center to a side is an apothem. The picture below illustrates these definitions. The picture below illustrates finding the area to an equilateral triangle:.
Students should be able to find the area of various regular polygons if they have enough information about the figure, such as angles measures, length of the center, the radius, or the length of a side.
Click here to check yourself. This concludes lesson 1 on area. You should now be able to find the area of various types of geometric figures.
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