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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

**Calculate circumference.**Perimeter is the sum of the lengths of the outer faces of any plane geometry. For a regular polygon, the perimeter can be calculated by multiplying the length of a side by its number of sides (

*n*).

^{[1] X Research Source}

**Define the midline.**The midline of a regular polygon is a perpendicular segment from its center to one of its sides. The midline is a bit more difficult to calculate than the circumference.

- 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*).

**Know the correct formula.**The area of any regular polygon is calculated using the formula:

**Area = (**, where

*a*x*p*)/2**a**is the length of the midline and

**p**is the perimeter of the polygon.

**Assign the**

**a**and

**p**values to the formula and calculate the area. For example, we have a hexagon (6 sides) with each side (

*s*) having a length of 10.

- 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

**Understand that every regular polygon can be thought of as a set of triangles.**Each side of the polygon represents the base edge of the triangle, and the number of sides of the polygon is the number of triangles contained in that polygon. Each triangle has the same base length, height, and area.

^{[2] X Research Source}

**Remember the formula for calculating the area of a triangle.**The area of any triangle is 1/2 the product of the base (here the side of the polygon) and the height (which is the midline of the regular polygon).

^{[3] X Research Sources}

**Analyze similarities.**Again, the formula for a regular polygon is 1/2 the product of the midline and the perimeter. The perimeter of the polygon is the product of the length of each side times the number of sides (

*n*); for a regular polygon,

*n*also represents the number of triangles constituting that polygon. So, this formula is nothing more than the sum of the areas of all the triangles inside that polygon.

^{[4] X Research Sources}

## 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.

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