A regular polygon has all sides (and angles) equal length and size.
These are all regular polygons.
An irregular polygon has some sides (and angles) of different lengths and sizes.
These are all irregular polygons.
The word polygon comes from the Greek poly - meaning many and gonos - meaning angles. So a polygon is a many angled figure.
With many angles comes many sides, in fact, every 2D straight-sided shape has the same number of angles as sides.
Let's have a look at convex shapes first:
Here are some concave shapes:
A convex shape can be identified through two key elements:
Which of the following shapes are concave/non-convex?
Different sided figures have names that describe the number of angles and sides.
Angle sum of an $n$n-sided polygon is $\left(n-2\right)\times180$(n−2)×180 degrees The angles inside a quadrilateral will add up to $\left(4-2\right)\times180=360$(4−2)×180=360 degrees The angles inside a hexagon will add up to $\left(6-2\right)\times180=720$(6−2)×180=720 degrees The angles inside an octagon will add up to $\left(8-2\right)\times180=1080$(8−2)×180=1080 degrees |
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Sum of exterior angles of any polygon is $360^\circ$360°
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Neil claims to have drawn a regular polygon with each exterior angle equal to $45^\circ$45°.
First find $n$n, the number of sides of such a polygon.
Hence what type of shapes is this ?
Octagon
Nonagon
Decagon
Hexagon
This shape cannot exist
Heptagon
Consider the adjacent quadrilateral.
Find the value of the angle marked $x$x.
Find the value of the angle marked $a$a.
Find the value of the angle marked $b$b.
Find the value of the angle marked $c$c.
Find the value of the angle marked $d$d.
The sum of exterior angles in a quadrilateral is $\editable{}$°
Triangles are three-sided shapes and have the following properties:
Angle sum of a triangle is $180^\circ$180° | |
Base angles are equal in an isosceles triangle
Sides opposite base angles are equal in an isosceles triangle |
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All angles in an equilateral triangles are equal
All angles in an equilateral triangle are equal to $60^\circ$60° All sides in an equilateral triangle are equal |
Based on the length of the sides, choose the most appropriate classification for the triangles as scalene, isosceles, or equilateral.
Isosceles
Equilateral
Scalene
Isosceles
Scalene
Equilateral
Equilateral
Isosceles
Scalene
Scalene
Equilateral
Isosceles
Isosceles
Equilateral
Scalene
Isosceles
Equilateral
Scalene
Quadrilaterals are four-sided shapes and have the following properties:
Angle sum of a quadrilateral is $360^\circ$360°.
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Parallelogram
Rectangle
Square
Rhombus
Trapezium
Kite
Based on the length of each side, classify the following as a kite, rectangle or square.
Choose the most precise answer.
Rectangle
Square
Kite
Rectangle
Kite
Square
Square
Kite
Rectangle
Square
Rectangle
Kite
Kite
Square
Rectangle
Kite
Square
Rectangle
Which of the following is true?
A square is a rhombus.
A trapezium is a parallelogram.
A parallelogram is a rectangle.
A kite is a rhombus.
A rhombus is a square.