The Formula For Area Of N Sided Polygon Explained In Simple Terms
Are you struggling with finding the area of a polygon with more than 4 sides? Fear not, as in this article we will explore the formula for calculating the area of n sided polygons in easy and simple terms. Whether you are a student or a professional, this article will provide you with the necessary tools to solve any polygon area problem with ease.
What is a Polygon?
A polygon is a two-dimensional figure that is made up of straight lines and has three or more sides. Examples of polygons include triangles, squares, rectangles, and pentagons. The area of a polygon is the amount of space inside the polygon.
Formula for Area of a Regular Polygon
A regular polygon is a polygon with all sides and angles equal. The formula for calculating the area of a regular polygon is:
Area = 1/2 * Perimeter * Apothem
Where the perimeter is the sum of all sides of the polygon, and the apothem is the distance between the center of the polygon and the midpoint of any side. Let's take a look at an example:
Example: Find the area of a regular hexagon with a side length of 5 cm.
Step 1: Calculate the perimeter of the hexagon. Since a hexagon has 6 sides, the perimeter is 6 times the length of one side, which is 5 cm. Therefore, the perimeter is 30 cm.
Step 2: Calculate the apothem of the hexagon. The apothem is the distance between the center of the hexagon and the midpoint of any side. Since the hexagon is regular, the apothem is also the radius of the inscribed circle. The radius of the inscribed circle can be found using the formula:
Radius = 1/2 * Side Length * tan(180/n)
Where n is the number of sides of the polygon. In this case, n is 6, so:
Radius = 1/2 * 5 cm * tan(180/6) = 2.88 cm
Therefore, the apothem is 2.88 cm.
Step 3: Use the formula to calculate the area of the hexagon.
Area = 1/2 * Perimeter * Apothem = 1/2 * 30 cm * 2.88 cm = 43.2 cm2
Therefore, the area of the regular hexagon is 43.2 cm2.
Formula for Area of an Irregular Polygon
An irregular polygon is a polygon with sides and angles that are not equal. To calculate the area of an irregular polygon, we need to divide the polygon into smaller shapes with known areas, such as triangles or rectangles, and then add up the areas of these shapes. Let's take a look at an example:
Example: Find the area of an irregular pentagon with sides of lengths 6 cm, 8 cm, 7 cm, 9 cm, and 5 cm.
Step 1: Divide the pentagon into triangles. We can draw lines from one vertex to the opposite side to create three triangles.
Step 2: Calculate the area of each triangle. We can use the formula for the area of a triangle:
Area = 1/2 * Base * Height
Where the base is one side of the triangle, and the height is the perpendicular distance from the base to the opposite vertex. We can use the Pythagorean theorem to calculate the height of each triangle.
Triangle 1:
Base = 6 cm
Height = √(8 cm)2 - (3 cm)2 = √55 cm ≈ 7.42 cm
Area = 1/2 * 6 cm * 7.42 cm ≈ 22.26 cm2
Triangle 2:
Base = 7 cm
Height = √(5 cm)2 - (2.5 cm)2 = √18.75 cm ≈ 4.33 cm
Area = 1/2 * 7 cm * 4.33 cm ≈ 15.16 cm2
Triangle 3:
Base = 9 cm
Height = √(8 cm)2 - (4 cm)2 = √48 cm ≈ 6.93 cm
Area = 1/2 * 9 cm * 6.93 cm ≈ 31.19 cm2
Step 3: Add up the areas of the triangles.
Total Area = 22.26 cm2 + 15.16 cm2 + 31.19 cm2 = 68.61 cm2
Therefore, the area of the irregular pentagon is approximately 68.61 cm2.
Conclusion
Calculating the area of a polygon with more than 4 sides may seem daunting, but with the right formula and some basic geometry knowledge, it can be easily done. Whether you are dealing with a regular or an irregular polygon, the key is to break it down into smaller shapes with known areas, such as triangles or rectangles. By following the steps outlined in this article, you can solve any polygon area problem with ease.
So, next time you are faced with a polygon area problem, remember the formula for calculating the area of a regular polygon and the method for calculating the area of an irregular polygon. Happy calculating!
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