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What are polygons?
Polygons are two dimensional closed shapes made up of segments of straight lines.
The word polygon originates from the Greek words poly which means many and gon which means angle. Putting the two words together, polygon means having many angles.
2. Categories of polygons
Regular and irregular polygons
A polygon is said to be regular when it has equal lengths of (all) sides and (all) equal angles. If the sides or the angles are not the same, it is an irregular polygon.
Concave and convex polygons
A polygon is said to be concave when any interior angle is greater than 180°.
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A concave polygon
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A polygon is said to be convex when there is no interior angle greater than 180°. In other words, a convex polygon does not have any angles pointing inwards.
Simple and complex polygons
The sides/lines of a simple polygon do not cross. The sides/lines of a complex polygon intersects.
3. Interior angles
Interior angles are angles inside a polygon. For instance, a triangle has three angles and a quadrilateral has four angles. The sum of the angles of a triangle is 180°. The sum of the angles of a quadrilateral is 360°.
In general, for a polygon with
n number of sides, the sum of interior angles is n-2×180°
For a regular polygon, the value of each angle is
\({n-2×(180°) \over n}\)
Note that the above formula cannot be used to calculate the value of each angle of an irregular polygon because the angles may not be the same.
Some polygons have special names. The table below displays the names of polygons with n=3 to n=10.
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n
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Name
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3
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Triangle
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4
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Quadrilateral
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5
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Pentagon
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6
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Hexagon
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7
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Heptagon
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8
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Octagon
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9
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Nonagon
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10
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Decagon
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Tag
Secondary school
Polygons
Reflection
What are polygons?
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How are polygons categorized?
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How do you calculate the interior angles of a polygon
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Which is not the characteristic of a polygon?
Given P is a polygon with eight sides, what is the sum of the interior angles?
If the polygon P above is a regular polygon, what is the value of each angle in the polygon?
What is the smallest possible value of n where n is the number of sides of a polygon?
What is the name of the polygon with eight sides?
Define polygons.
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What are the different categories of polygons?
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What is the formula to calculate the sum of the interior angles of a polygon?
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What is the formula to calculate each angle of a regular polygon?
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