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X sides polygon11/15/2023 ![]() ![]() The sum of the interior angles is not quite so straightforward, but it is still quite a simple formula. The diagram shows the sum of the exterior angle of a 5-sided polygon, or pentagon, which is 360° (the same as any polygon).Įach exterior angle of a regular pentagon is 360°/5, or 72°. Now let's make the shape very small, so you can hardly see it:Īgain, this illustrates that the sum of the exterior angles of a polygon is 360°.įor a regular polygon, each exterior angle is the same, so each angle of an n-sided polygon is 360°/n. Let's take the previous diagram and make the polygon smaller:Īlthough the shape is smaller, it is still the same shape, so the exterior angles are still the same. Therefore the sum of the exterior angles in a polygon is 360°. But after the ant has gone all the way around the shape it will be facing the same way as it was when it started, which means it has turned through 360°. Let’s see some properties of irregular polygons. It will turn through the exterior angle of that corner, so it faces in the correct direction to walk along the next side.īy the time the ant gets all the way around the shape it will have turned at each corner, so the total angle it has turned through will be the sum of the exterior angles of the shape. Here are a few examples showing the names of irregular polygons and the number of sides: Properties of Irregular Polygons. Each time it reaches a corner, the ant will turn to its right. ![]() In fact it is a 4-sided polygon, just like a triangle is a 3-sided polygon, a pentagon is a 5-sided polygon, and so on. ![]() The formulas below give the length of the side of regular polygon given the number of sides and either the radius or apothem. A polygon is a 2D shape with straight sides. Oh Yes when two sides cross over, we call it a 'Complex' or 'Self-Intersecting' quadrilateral, like these: They still have 4 sides, but two sides cross over. That is '3' less than the number of sides. Another way to express the general rule for the total number of diagonals is to think about the number of diagonals that can be drawn from each vertex in a polygon. Try this Adjust the regular polygon below by dragging any orange dot, or alter the number of sides. Since there are n sides, the remaining n (n 1) / 2 n n(n-1)/2 -n n (n 1) /2 n of them are the diagonals of a convex polygon. To see why this is the case, imagine an ant crawling round the outside of the shape. The sides of a regular polygon are the line segments that make it up. It doesn't matter how many sides the shape has, the sum of the exterior angles is always the same. The sum of the exterior angles in a polygon is always 360°. We can do this for each side of the shape: If we extend one of the sides of a polygon, the angle between the extended side and the side next to it is called an exterior angle. Here is a 5-sided, irregular polygon, showing its interior angles: The angles inside a polygon are called its interior angles. They are also covered in this video: Interior angles of a polygon I'm then using the technique discussed here to generate faces on the N-gon.Here are some basic geometry rules about the interior and exterior angles of a polygon. I'm using the solution discussed here to calculate the vertices of the N-gon. The long-term goal is to use this as the first step in rendering a polyhedral prism. I'm using Three.js to procedurally generate a regular N-gon based on a user-provided number of sides. ![]()
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