Tessellations

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You will be awarded a trophy if you get at least 7 questions correct and you do this activity online.

1

Which regular polygons tessellate?

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2

Imagine a tessellation of trapezia where each edge of one trapezium is aligned along an edge of the same length of another trapezium. How many trapezia will meet at any junction point in the tessellation?

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3

Imagine a tessellation of scalene triangles where each edge of one triangle is aligned along an edge of the same length of another triangle. How many triangles will meet at any junction point in the tessellation?

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4

Tessellations can be made using two different regular polygons. Which other polygon would complete a tessellation including octagons?

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5

Tessellations can be made using two different regular polygons. Which other polygon would complete a tessellation including dodecagons?

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6

Which pentominoes tessellate?

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7

Which 7-pin polygons tessellate?

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8

What is the sum of the angles (in degrees) of the vertices that come together at a point in an edge-to-edge tessellation?

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9

In a particular semiregular tessellation four regular shapes come together at each point. If two of the shapes are squares, the third is a triangle, what is the name of the fourth polygon?

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10

In a different semiregular tessellation three regular shapes come together at each point. If one of the shapes is a square, the second is a hexagon, what is the name of the third polygon?

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Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

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Description of Levels

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Level 1 - General tesselations quiz

Level 2 - Finding algles in semiregular tessellations

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

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Example

You may also want to use a calculator to check your working. See Calculator Workout skill ##.

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