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Polygons

Definition: A plane figure that are bounded by straight lines

2 types of polygons:

Irregular and Regular Polygons

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Regular Polygons is a polygon that all angles are equal in measure, and equilateral - all sides have the same length!

Irregular polygons are polygons that does not have all its sides equal and not all the angles are equal in measure

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IMPORTANT → THE SUM OF ALL THE EXTERIOR OF A REGULAR POLYGON IS ALWAYS 360 DEGREES

Interior and Exterior Angles:

Any angle that is on the inside of a shape is called an interior angle.

Any angle that is on the outside of a shape is called an exterior angle.

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Formulas:

Calculate sum of interior angles

(n-2) * 180

→ n = number of sides

Calculate each exterior angle

360/n

→ n = number of sides

Calculate number of sides

360/exterior angle

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PERIMETER

Definition : outline of a shape

Triangles

P = a+b+c

==> Perimeter = Length 1 + Length 2 + Length 3

Square

P = 4a

==> Perimeter = Length * 4

Rectangle

P = 2a + 2b

==> Perimeter =( Longer length + Shorter length)*2

Parallelogram

P = 2a + 2b

==> Perimeter = (Long side * 2) + (Short side *2)

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AREA

Definition : the total space taken up by a shape

Triangles

Base*Height/2

Square

a²

Rectangle (or any other irregular polygons)(except trapezium)

Base * Height

Trapezium

(B1 + B2)/2 * H

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Tessellation:

A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps

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Polygons that tessellates are:

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To find out if a polygon can tessellate, we need to find the each interior angle. If it is a factor of 360, the polygon will tessellate.

For example: Triangle

Interior angle:

= (n-2)*180

= (3-2)*180

= 1*180

= 180

Now we take the interior angle, and divide it by the number of sides.

= 180/3

= 60

Is 60 a factor of 360?

→ Yes

Because 60*6 = 360

So a triangle does tessellate.

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