Polygon assessment

POLY

GON ASSESSMENT:

TAKE A

REGULA

R AND A

SEMI R

EGULAR

TESSELL

ATIO

N AND, U

SING T

ECHNOLOGY,

EXPLAIN

WHY

IT T

ESSELLAT

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AN

AS

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I A G

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Sum of interior angles of a regular hexagon=720o

120°

120°

120°120°

120°120°

The interior angle of a regular hexagon is 120o.

Take a regular hexagon.

We find that the diagonals intersect.

When the diagonals at the point of intersection are measured, we find that the angles amount to 360o.

This is also found to be the case with other regular polygons (either by measuring the angles at the point of intersection or measuring the angles of intersection when the polygon is rotated around a fixed point-a tessellation).

(Triangle)

(Square)

However, this is not the case for all regular polygons.

(Pentagon)

(Diagonals at point of intersection)

(Tessellation: Non-regular)

(Diagonals)

(Tessellation: Semi-regular, not regular)

(Octagon)

As mentioned before, a shape tessellates if it can fit repeatedly into a pattern around a central point without overlapping points or gaps.

As you can see from the Octagon:

Its intersecting angles equal 360o, but cannot tessellate:

This is because of its interior angle.

Each interior angle of a regular shape is equal. This angle, multiplied by the amount of sides the shape has, is its angle sum:

For a shape to be able to tessellate, the total angle sum created by rotating the shape around a single point must equal 3600.

If the angle sum of the interior angles around that center point does not equal 360o, then either a gap or an overlap is created, and the shape cannot tessellate.

135o + 135o135o=405o

Computer Applications Used:

Geometer’s Sketch Pad 5

And:

Microsoft Powerpoint