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How do you know if a polygon is regular? If the given polygon contains equal sides and equal angles, then we can say that the given polygon is regular; otherwise, it is irregular. Q4
- Trigonometric Identities
Trigonometric Identities are useful whenever trigonometric...
- Two Lines
Let us do an activity to obtain a figure with two lines of...
- Trigonometric Identities
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How do you know if a polygon is regular?
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How do you classify a regular polygon?
- 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?
A regular polygon is a closed, straight-sided figure that has equal side and angle measurements. If a polygon does not have all equal sides and interior angles, it is an irregular polygon. For example, Regular quadrilateral: Irregular quadrilateral: All the sides are the same length.
Regular or Irregular. A regular polygon has all angles equal and all sides equal, otherwise it is irregular. Concave or Convex. A convex polygon has no angles pointing inwards. More precisely, no internal angle can be more than 180°. If any internal angle is greater than 180° then the polygon is concave. ( Think: concave has a "cave" in it)
Play. Identify Polygons and Quadrilaterals Game. Play. Identify the LInes of Symmetry in Irregular Shapes Game. Play. More Games. Parts of a Polygon. A polygon has three parts: Sides: A line segment that joins two vertices is known as a side. Vertices: The point at which two sides meet is known as a vertex. Angles: interior and exterior.
Nov 28, 2020 · The answer is that the polygon is a regular hexagon. When lines intersect in the geometric plane, they form polygons. Apply what you know in order to classify these polygons.
Types of Polygon; How do you know if a Polygon is Regular? Any polygon is a regular polygon if it satisfies the following criteria: The length of all its sides must be equal. All interior angles must measure the same. All the exterior angles must measure the same. What is the Interior Angle of a Regular Polygon?
