This page examines the nature of two-dimensional or ‘plane’ polygons. A polygon is any kind of shape consisted of of right lines that have the right to be drawn on a level surface, prefer a piece of paper. Such shapes encompass squares, rectangles, triangles and pentagons yet not circles or any type of other form that has a curve.
You are watching: A three sided regular polygon is called equilateral
Understanding shapes is important in mathematics. Girlfriend will definitely be required to learn about shapes in ~ school yet understanding the nature of shapes has plenty of practical applications in professional and also real-life cases too.
Many experts need to know the properties of shapes, including engineers, architects, artists, real-estate agents, farmers and construction workers.
You might well need to understand shapes when doing residence improvements and DIY, as soon as gardening and also even when planning a party.
When working v polygons the key properties i beg your pardon are important are:The number of sides the the shape. The angles in between the sides of the shape. The length that the sides of the shape.
Number the Sides
Polygons space usually characterized by the number of sides that they have.
Three-Sided Polygons: Triangles
A three-sided polygon is a triangle. there are several different types of triangle (see diagram), including:Equilateral – every the sides room equal lengths, and also all the interior angles are 60°. Isosceles – has two same sides, v the 3rd one a various length. 2 of the interior angles are equal. Scalene – all 3 sides, and also all three internal angles, are different.
Triangles can likewise be defined in terms of their internal angles (see our page on Angles for an ext about naming angles). The internal angles that a triangle always include up come 180°.
A triangle through onlyacuteinternal angles is referred to as an acute (or acute-angled) triangle. One with oneobtuseangle and also two acute angle is dubbed obtuse (obtuse-angled), and also one through aright angleis recognized as right-angled.
Each that these will certainly also be one of two people equilateral, isosceles or scalene.
Four-Sided polygon - Quadrilaterals
Four-sided polygons room usually described as quadrilaterals, quadrangles or occasionally tetragons. In geometry the term quadrilateral is generally used.
The term quadrangle is frequently used to describe a rectangular enclosed outdoor space, for example ‘the freshers assembled in the university quadrangle’. The term tetragon is continuous with polygon, pentagon etc. You may come throughout it occasionally, yet it is not generally used in practice.
The family of quadrilaterals contains the square, rectangle, rhombus and also other parallelograms, trapezium/trapezoid and kite.
The interior angles of all quadrilaterals add up come 360°.
Square: four sides of equal length, 4 internal best angles.
Rectangle: 4 internal appropriate angles, opposite sides of same length.
Parallelogram: the opposite sides space parallel, the opposite sides are equal in length, the opposite angles are equal.
Rhombus: A special form of parallel in i m sorry all 4 sides room the very same length, prefer a square that has actually been squashed sideways.
Trapezium (or trapezoid): two sides room parallel, but the other two sides space not. Next lengths and also angles are not equal.
Isosceles Trapezium (or trapezoid): two sides space parallel and also base angles are equal, an interpretation that non-parallel sides are additionally equal in length.
Kite: 2 pairs of nearby sides are of equal length; the shape has actually an axis of symmetry.
Irregular Quadrilateral: a four-sided form where no sides are equal in length and no inner angles room the same. All inner angles still include up to 360°, as with all other continual quadrilaterals.
More than 4 Sides
A five-sided form is dubbed a pentagon.
A six-sided shape is a hexagon, a seven-sided form a heptagon, when an octagon has actually eight sides…
The name of polygons are acquired from the prefixes of old Greek numbers. The Greek numerical prefix occurs in numerous names of daily objects and concepts. These deserve to sometimes be useful in helping you remember how plenty of sides a polygon has. Because that example:an octopus has eight legs – one octagon has eight sides. A decade is ten year – a decagon has ten sides. The modern pentathlon has actually five occasions – a pentagon has five sides. An Olympic heptathlon has seven events – a heptagon has seven sides.
The ‘poly-‘ prefix simply means ‘multiple’, therefore a polygon is a shape with multiple sides, in the same method that ‘polygamy’ means multiple spouses.
There space names for plenty of different types of polygons, and also usually the variety of sides is an ext important 보다 the surname of the shape.
There are two main types of polygon - regular and also irregular.
A regular polygon has actually equal size sides with equal angles in between each side. Any type of other polygon is one irregular polygon, which by an interpretation has unequal length sides and unequal angles in between sides.
Circles and also shapes that incorporate curves space not polygons - a polygon, by definition, is comprised of right lines. See our pages top top circles and also curved shapes for more.
Angles between Sides
The angles between the sides of shapes are important when defining and also working through polygons. Check out our web page on angles for an ext about just how to measure angles.
There is a advantageous formula for finding out the complete (or sum) of internal angles for any polygon, the is:
(number of political parties - 2) × 180°
For a pentagon (a five-sided shape) the calculation would certainly be:
5 - 2 = 3
3 × 180 = 540°.
The sum of interior angles for any (not complex) pentagon is 540°.
Furthermore, if the shape is a regular polygon (all angles and also length the sides are equal) climate you have the right to simply divide the sum of the inner angles by the number of sides to uncover each interior angle.
540 ÷ 5 = 108°.
A regular pentagon as such has 5 angles each equal to 108°.
The size of the Sides
As well together the variety of sides and the angles in between sides, the size of every side of forms is additionally important.
The size of the sides of a plane shape allows you to calculate the shape’s perimeter (the distance around the external of the shape) and also area (the quantity of space inside the shape).
If your shape is a continuous polygon (such as a square in the example above) climate it is only important to measure one side as, by definition, the other sides of a regular polygon space the very same length. It is common to use tick clues to show that every sides space an same length.
In the example of the rectangle we needed to measure 2 sides - the 2 unmeasured sides space equal come the two measured sides.
It is typical for some dimensions no to be presented for more complex shapes. In together cases missing dimensions can be calculated.
In the example above, 2 lengths room missing.
The missing horizontal length deserve to be calculated. Take the shorter horizontal known length native the longer horizontal well-known length.
9m - 5.5m = 3.5m.
The exact same principle can be offered to job-related out the missing vertical length. The is:
3m - 1m = 2m.
Bringing every the details Together: Calculating the Area of Polygons
The simplest and also most an easy polygon for the functions of calculating area is the quadrilateral. To achieve the area, you merely multiple size by upright height.
For parallelograms, note that vertical height is NOT the size of the sloping side, yet the upright distance between the two horizontal lines.
This is due to the fact that a parallel is essentially a rectangle with a triangle reduced off one end and also pasted onto the other:
You have the right to see that if you remove the left-hand blue triangle, and also stick the onto the other end, the rectangle becomes a parallelogram.
The area is length (the top horizontal line) multiplied by height, the upright distance in between the 2 horizontal lines.
To job-related out the area of a triangle, girlfriend multiple length by vertical elevation (that is, the vertical elevation from the bottom heat to the optimal point), and halve it. This is essentially since a triangle is fifty percent a rectangle.
To calculation the area of any kind of regular polygon, the easiest way is to divide it into triangles, and use the formula for the area the a triangle.
So, for a hexagon, because that example:
You deserve to see indigenous the diagram the there are six triangles.
The area is:
Height (red line) × size of next (blue line) × 0.5 × 6 (because there are 6 triangles).
You can likewise work out the area of any type of regular polygon utilizing trigonometry, yet that’s rather much more complicated.
See our page Calculating Area because that more, consisting of examples.
You can also work out the area of any kind of regular polygon using trigonometry, yet that’s rather an ext complicated. Watch our Introduction come Trigonometry page for more information.
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Continue to: Calculating AreaCurved Shapes
See also:Three-Dimensional shapes | Area, surface Area and also Volume recommendation Sheet simple Transformations that 2-Dimensional shapes | confident and negative Numbers
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