In geometry, a polygon is a closed shape that has straight sides. Calculating the area of a polygon can be done using various methods depending on the number of sides it has and the information provided. In this article, we will discuss how to find the area of a polygon given below and explore different techniques to calculate its area.
Definition of Polygon
A polygon is a two-dimensional shape that is formed by connecting straight line segments to create a closed figure. The sides of a polygon do not intersect, and the angles between the sides are always less than 180 degrees. Examples of polygons include triangles, squares, pentagons, and hexagons.
Given Polygon
For the purpose of this article, let’s consider a given polygon with the following properties:
- Number of sides: 5
- Side lengths: 8 cm, 10 cm, 7 cm, 9 cm, 6 cm
- Regular or irregular: Irregular
Calculating Area of the Polygon
There are several methods to calculate the area of a polygon, depending on its properties. In the case of an irregular polygon like the one given above, we can use the following formula:
Area of Irregular Polygon = (1/2) * |(x1*y2 + x2*y3 + … + xn*y1) – (y1*x2 + y2*x3 + … + yn*x1)|
where (x1, y1), (x2, y2), …, (xn, yn) are the coordinates of the vertices of the polygon in order.
Calculations
Using the side lengths provided for the polygon, we can calculate the area using the formula mentioned above. Let’s substitute the values into the formula:
Area = (1/2) * |(8*10 + 10*7 + 7*9 + 9*6 + 6*8) – (10*8 + 7*9 + 9*6 + 6*8 + 8*7)|
Area = (1/2) * |(80 + 70 + 63 + 54 + 48) – (80 + 63 + 54 + 48 + 56)|
Area = (1/2) * |315 – 301|
Area = (1/2) * 14
Area = 7 cm²
Conclusion
In conclusion, we have calculated the area of the given irregular polygon to be 7 cm². By using the formula for calculating the area of an irregular polygon, we can determine the space enclosed within its boundaries. It is essential to understand the properties of the polygon and use the appropriate formulas to accurately find its area.
