How Do You Draw Two Different Polygons That Have 4 Sides And 4 Angles
This page examines the backdrop of two-dimensional or 'plane' polygons. A polygon is any shape made upwards of straight lines that can be drawn on a flat surface, similar a piece of newspaper. Such shapes include squares, rectangles, triangles and pentagons but not circles or any other shape that includes a curve.
Agreement shapes is of import in mathematics. You will certainly be required to learn about shapes at school merely understanding the properties of shapes has many practical applications in professional and real-life situations too.
Many professionals need to understand the backdrop of shapes, including engineers, architects, artists, existent-estate agents, farmers and construction workers.
Yous may well demand to sympathise shapes when doing home improvements and DIY, when gardening and fifty-fifty when planning a political party.
When working with polygons the principal properties which are important are:
- The number of sides of the shape.
- The angles between the sides of the shape.
- The length of the sides of the shape.
Number of Sides
Polygons are usually divers past the number of sides that they take.
Three-Sided Polygons: Triangles
A three-sided polygon is a triangle. There are several different types of triangle (see diagram), including:
- Equilateral – all the sides are equal lengths, and all the internal angles are 60°.
- Isosceles – has two equal sides, with the third i a different length. Two of the internal angles are equal.
- Scalene – all three sides, and all three internal angles, are unlike.
Triangles can also be described in terms of their internal angles (see our folio on Angles for more nigh naming angles). The internal angles of a triangle always add upwards to 180°.
A triangle with onlyacute internal angles is called an acute (or acute-angled) triangle. One with onebirdbrained angle and 2 acute angles is called obtuse (obtuse-angled), and one with aright bending is known equally right-angled.
Each of these will as well be either equilateral, isosceles or scalene.
Four-Sided Polygons - Quadrilaterals
Iv-sided polygons are commonly referred to as quadrilaterals, quadrangles or sometimes tetragons. In geometry the term quadrilateral is usually used.
The term quadrangle is oftentimes used to depict a rectangular enclosed outdoor infinite, for example 'the freshers assembled in the higher quadrangle'. The term tetragon is consistent with polygon, pentagon etc. You lot may come up across it occasionally, but it is not commonly used in practise.
The family of quadrilaterals includes the foursquare, rectangle, rhombus and other parallelograms, trapezium/trapezoid and kite.
The internal angles of all quadrilaterals add upwardly to 360°.
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Foursquare: Four sides of equal length, 4 internal correct angles.
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Rectangle: Four internal right angles, opposite sides of equal length.
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Parallelogram: Opposite sides are parallel, reverse sides are equal in length, opposite angles are equal.
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Rhombus: A special type of parallelogram in which all 4 sides are the same length, like a square that has been squashed sideways.
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Trapezium (or trapezoid): Ii sides are parallel, but the other two sides are not. Side lengths and angles are not equal.
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Isosceles Trapezium (or trapezoid): Ii sides are parallel and base of operations angles are equal, meaning that non-parallel sides are also equal in length.
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Kite: Two pairs of adjacent sides are of equal length; the shape has an axis of symmetry.
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Irregular Quadrilateral: a four-sided shape where no sides are equal in length and no internal angles are the same. All internal angles yet add up to 360°, as with all other regular quadrilaterals.
More than Four Sides
A five-sided shape is called a pentagon.
A six-sided shape is a hexagon, a seven-sided shape a heptagon, while an octagon has viii sides…
Polygon Names
The names of polygons are derived from the prefixes of ancient Greek numbers. The Greek numerical prefix occurs in many names of everyday objects and concepts. These tin sometimes be useful in helping you remember how many sides a polygon has. For case:
- An octopus has eight legs – an octagon has viii sides.
- A decade is 10 years – a decagon has 10 sides.
- The modern pentathlon has five events – a pentagon has five sides.
- An Olympic heptathlon has seven events – a heptagon has seven sides.
The 'poly-' prefix simply means 'multiple', then a polygon is a shape with multiple sides, in the same manner that 'polygamy' ways multiple spouses.
There are names for many different types of polygons, and ordinarily the number of sides is more important than the proper name of the shape.
At that place are two chief types of polygon - regular and irregular.
A regular polygon has equal length sides with equal angles between each side. Any other polygon is an irregular polygon, which by definition has unequal length sides and diff angles between sides.
Circles and shapes that include curves are non polygons - a polygon, by definition, is made up of straight lines. Come across our pages on circles and curved shapes for more than.
Angles Between Sides
The angles betwixt the sides of shapes are important when defining and working with polygons. See our page on Angles for more almost how to measure out angles.
There is a useful formula for finding out the total (or sum) of internal angles for whatsoever polygon, that is:
(number of sides - 2) × 180°
Example:
For a pentagon (a five-sided shape) the calculation would be:
v - ii = 3
3 × 180 = 540°.
The sum of internal angles for any (not circuitous) pentagon is 540°.
Furthermore, if the shape is a regular polygon (all angles and length of sides are equal) then you tin simply separate the sum of the internal angles by the number of sides to find each internal angle.
540 ÷ 5 = 108°.
A regular pentagon therefore has 5 angles each equal to 108°.
The Length of the Sides
As well as the number of sides and the angles betwixt sides, the length of each side of shapes is likewise important.
The length of the sides of a plane shape enables you to calculate the shape's perimeter (the distance around the outside of the shape) and area (the amount of infinite inside the shape).
If your shape is a regular polygon (such as a square in the example above) so it is only necessary to measure i side as, past definition, the other sides of a regular polygon are the same length. It is mutual to use tick marks to testify that all sides are an equal length.
In the example of the rectangle we needed to measure 2 sides - the two unmeasured sides are equal to the two measured sides.
Information technology is common for some dimensions not to be shown for more circuitous shapes. In such cases missing dimensions can be calculated.
In the case in a higher place, two lengths are missing.
The missing horizontal length can exist calculated. Have the shorter horizontal known length from the longer horizontal known length.
9m - 5.5m = three.5m.
The same principle can exist used to piece of work out the missing vertical length. That is:
3m - 1m = 2m.
Bringing All the Information Together: Calculating the Area of Polygons
The simplest and well-nigh basic polygon for the purposes of calculating area is the quadrilateral. To obtain the area, yous merely multiple length by vertical elevation.
For parallelograms, note that vertical height is NOT the length of the sloping side, but the vertical altitude between the ii horizontal lines.
This is because a parallelogram is essentially a rectangle with a triangle cut off one end and pasted onto the other:
You tin can encounter that if you lot remove the left-hand blue triangle, and stick it onto the other stop, the rectangle becomes a parallelogram.
The area is length (the elevation horizontal line) multiplied by summit, the vertical distance betwixt the two horizontal lines.
To piece of work out the area of a triangle, you multiple length by vertical acme (that is, the vertical height from the bottom line to the top point), and halve information technology. This is essentially because a triangle is half a rectangle.
To calculate the area of whatever regular polygon, the easiest style is to divide it into triangles, and utilise the formula for the area of a triangle.
So, for a hexagon, for example:
You tin see from the diagram that there are six triangles.
The expanse is:
Superlative (red line) × length of side (blue line) × 0.5 × 6 (because at that place are six triangles).
You can also piece of work out the surface area of any regular polygon using trigonometry, but that'southward rather more complicated.
Come across our page Calculating Area for more, including examples.
You lot can also work out the expanse of any regular polygon using trigonometry, but that'south rather more complicated. Run across our Introduction to Trigonometry page for more information.
Source: https://www.skillsyouneed.com/num/polygons.html
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