Watch this video lesson to learn why a regular polygon makes your life easier when it comes to finding the area inside one.
Learn the one formula for area that will work for any type of regular polygon.
A Regular Polygon
Regular polygons are everywhere! Just look around you, and you will see them, especially when you’re driving around. Look at a stop sign or a yield sign, and you are looking at a regular polygon. Defined, a regular polygon is a flat shape with straight sides whose sides and angles are all equal. These types of shapes all sort of look like they want to be circles.
It almost looks like each corner of the shape is reaching out as far as it can to touch the circle. And if you drew a circle around each shape, you would see that each corner actually does touch the circle. Try it for yourself and see.
Sides
In this lesson, we are going to find the area of a regular polygon.
To do this, one of the things we need to know is the number of sides our regular polygon has. We usually call this number n in formulas. We leave it as n because this number changes depending on what kind of regular polygon we have. The kind is determined by how many sides it has.So, a regular polygon with 8 sides will have the n equal to 8, and we would plug in 8 wherever we see the n in formulas.We also need to know the length of each side.
Because all the sides of a regular polygon are equal, we just need to know the length of one side.
The Apothem
Another measurement that we need for the area is the apothem, the distance from the center of a regular polygon to the middle of any of its sides. If we drew a line from each corner of a regular polygon to the center, we will have broken our regular polygon into a number of small triangles. The apothem can then be likened to the height of each of these small triangles.
Finding the Area Using the Apothem
The formula to find the area of any regular polygon is this:Area of Regular Polygon = n * (side length) * (apothem) / 2So, this formula is telling us to multiply the apothem, the number of sides, and the length of a side together and then to divide by 2. Let’s see how this works with a sample polygon.
Circumcircles has a center point and a radius.
