Search results
If it is a Regular Polygon (all sides are equal, all angles are equal) Shape Sides Sum of Interior Angles Shape Each Angle; Triangle: 3: 180° 60° Quadrilateral: 4: 360° 90° Pentagon: 5: 540° 108° Hexagon: 6: 720° 120° Heptagon (or Septagon) 7: 900° 128.57...° Octagon: 8: 1080° 135° Nonagon: 9: 1260° 140°..... Any Polygon: n (n−2 ...
- Regular Polygon
We can learn a lot about regular polygons by breaking them...
- Hexagon
Interior Angles of 120° Exterior Angles of 60° Area =...
- Interior Angles
Interior Angle An Interior Angle is an angle inside a shape....
- Pentagon
Properties. A regular pentagon has:. Interior Angles of...
- Exterior Angles
Exterior Angle The Exterior Angle is the angle between any...
- 2D Shapes
A polygon is a 2D shape with straight sides. To be a regular...
- Degrees
Angles can also be measured in Radians. (Note: "Degree" is...
- Regular Polygon
Jul 14, 2024 · Regular polygon formulas: sides, area, perimeter, angles. If you want to calculate the regular polygon parameters directly from equations, all you need to know is the polygon shape and its side length: 1. Area. area = n × a² × cot(π/n)/ 4. Where n - number of sides, a - side length.
- Polygon
- Properties
- "Circumcircle, Incircle, Radius and Apothem ..."
- Breaking Into Triangles
- A Smaller Triangle
- More Area Formulas
- A Table of Values
- Graph
A polygon is a planeshape (two-dimensional) with straight sides. Examples include triangles, quadrilaterals, pentagons, hexagons and so on.
So what can we know about regular polygons? First of all, we can work out angles. All the Exterior Angles of a polygon add up to 360°, so: Each exterior angle must be 360°/n (where nis the number of sides) Press play button to see. Interior Angle = 180° − Exterior Angle We know theExterior angle = 360°/n, so: Interior Angle = 180° − 360°/n And now ...
Sounds quite musical if you repeat it a few times, but they are just the names of the "outer" and "inner" circles (and each radius) that can be drawn on a polygon like this: The "outside" circle is called a circumcircle, and it connects all vertices (corner points) of the polygon. The radius of the circumcircle is also the radiusof the polygon. The...
We can learn a lot about regular polygons by breaking them into triangles like this: Notice that: 1. the "base" of the triangle is one side of the polygon. 2. the "height" of the triangle is the "Apothem" of the polygon Now, the area of a triangleis half of the base times height, so: Area of one triangle = base × height / 2 = side × apothem / 2 To ...
By cutting the triangle in half we get this: (Note: The angles are in radians, not degrees) The small triangle is right-angled and so we can use sine, cosine and tangent to find how the side, radius, apothem and n(number of sides) are related: There are a lot more relationships like those (most of them just "re-arrangements"), but those will do for...
We can use that to calculate the area when we only know the Apothem: And there are 2 such triangles per side, or 2n for the whole polygon: Area of Polygon = n × Apothem2 × tan(π/n) When we don't know the Apothem, we can use the same formula but re-worked for Radius or for Side: Area of Polygon = ½ × n × Radius2 × sin(2 × π/n) Area of Polygon = ¼ × ...
And here is a table of Side, Apothem and Area compared to a Radius of "1", using the formulas we have worked out:
And here is a graph of the table above, but with number of sides ("n") from 3 to 30. Notice that as "n" gets bigger, the Apothem is tending towards 1 (equal to the Radius) and that the Area is tending towards π= 3.14159..., just like a circle. What is the Side length tending towards?
Sum of the exterior angles of polygons = 360° So, each exterior angle = 360°n = 360°20 = 18° Example 4: The sum of the interior angles of a polygon is 1620°. How many sides does it have? Solution: Sum of the interior angles of a polygon with n sides = (n – 2) × 180° 1620° = (n – 2) × 180° n – 2 = 1620180. n – 2 = 9. n = 9 + 2 ...
- A diagonal of a polygon is a line segment connecting two non-consecutive vertices (corners).
- A Regular polygon has all sides of equal length and each angle also measures equal.
- Polygon is a closed shape made up of straight-line segments. The circle is a closed figure but it is made of a curve. So, a circle is not a polygon.
- A polygon must have a minimum of three sides.
- No, polygons have the same number of sides and angles because they are closed figures with non-intersecting lines.
Convex Polygon. If all the interior angles of a polygon are strictly less than 180 degrees, then it is known as a convex polygon. The vertex will point outwards from the centre of the shape. Concave Polygon. If one or more interior angles of a polygon are more than 180 degrees, then it is known as a concave polygon. A concave polygon can have ...
- 26 min
Feb 6, 2024 · Polygon Calculator. Use this calculator to calculate properties of a regular polygon. Enter any 1 variable plus the number of sides or the polygon name. Calculates side length, inradius (apothem), circumradius, area and perimeter. Calculate from an regular 3-gon up to a regular 1000-gon. Units: Note that units of length are shown for convenience.
People also ask
What are the different types of polygons?
What do we know about regular polygons?
How many triangles are there in a polygon?
How many vertices does a polygon have?
How many sides does a polygon have?
What is the exterior angle of a polygon?
Octagon. Octagons have 8 sides so again, we need to adjust the formula accordingly: sum of internal angles = (8 - 2) x 180°. 1080° = 6 x 180°. In a regular octagon, one angle would be worth ...
