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Calculating the area of a regular polygon is a fundamental concept in geometry. Regular polygons, characterized by their equal side lengths and interior angles, can vary in shape and size. However, the method for determining their area remains consistent. By breaking down the polygon into triangles and using basic trigonometric principles, we can accurately calculate the area enclosed by these intriguing shapes. In this guide, we will explore the step-by-step process of calculating the area of a regular polygon, equipping you with the necessary tools and understanding to tackle this mathematical problem with confidence.
This article was co-written by David Jia. David Jia is a tutoring teacher and founder of LA Math Tutoring, a private tutoring facility based in Los Angeles, California. With over 10 years of teaching experience, David teaches a wide variety of subjects to students of all ages and grades, as well as college admissions counseling and prep for SAT, ACT, ISEE, etc. scoring 800 in math and 690 in English on the SAT, David was awarded a Dickinson Scholarship to the University of Miami, where he graduated with a bachelor’s degree in business administration. Additionally, David has worked as an instructor in online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.
This article has been viewed 31,997 times.
A regular polygon is a two-dimensional geometry with equal sides and equal angles. Many polygons, such as rectangles or triangles, have fairly simple area formulas, but if you’re doing math with a polygon with more than four sides, it’s best to use the mids and the perimeters. vi of that figure. With a little effort, you will find out the area of a regular polygon in just a few minutes.
Steps
The area
- The formula to calculate the length of the median is: the length of the side ( s ) divided by all 2 times (tan) of the 180 degree quotient and the number of sides ( n ).
- The perimeter of the hexagon 6 x 10 ( n x s ) is 60 (so p = 60).
- To calculate the median using its own formula, we assign the values 6 and 10 to n and s . The result of the expression 2tan(180/6) will be 1.1547, then divide by 10 by 1.1547 to get 8.66.
- Area of the polygon: Area = a x p / 2, or 8.66 multiplied by 60 and divided by 2. The answer is 259.8 units.
- Note: there are no parentheses in the expression “Area”, so 8.66 divided by 2 and then multiplied by 60 or 60 divided by 2 and then multiplied by 8.66 gives the same result.
Understand the concept in a different way
Advice
- If the drawing of the octagon (or whatever shape) you are given is already divided into triangles and the area of a triangle is given, you do not need to find the midline. Just take the area of that triangle multiplied by the number of sides of the polygon.
This article was co-written by David Jia. David Jia is a tutoring teacher and founder of LA Math Tutoring, a private tutoring facility based in Los Angeles, California. With over 10 years of teaching experience, David teaches a wide variety of subjects to students of all ages and grades, as well as college admissions counseling and prep for SAT, ACT, ISEE, etc. scoring 800 in math and 690 in English on the SAT, David was awarded a Dickinson Scholarship to the University of Miami, where he graduated with a bachelor’s degree in business administration. Additionally, David has worked as an instructor in online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.
This article has been viewed 31,997 times.
A regular polygon is a two-dimensional geometry with equal sides and equal angles. Many polygons, such as rectangles or triangles, have fairly simple area formulas, but if you’re doing math with a polygon with more than four sides, it’s best to use the mids and the perimeters. vi of that figure. With a little effort, you will find out the area of a regular polygon in just a few minutes.
In conclusion, calculating the area of a regular polygon is a straightforward process that requires a few key steps. By first identifying the type of regular polygon and measuring its side length, one can use the appropriate formula to find the area. The process involves dividing the polygon into smaller shapes, such as triangles or rectangles, and finding the area of each individual shape. Finally, the areas of all the shapes are added together to determine the total area of the regular polygon. It is important to remember that the accuracy of the calculation relies on the precision of the measurements taken. By following these steps and using the correct formulas, anyone can easily calculate the area of a regular polygon and apply this knowledge to various practical applications.
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