Tessellations
Math ⇒ Geometry
Tessellations starts at 7 and continues till grade 12.
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See sample questions for grade 11
A semi-regular tessellation is made up of regular polygons. At each vertex, the arrangement is 3.6.3.6. What does this mean?
Calculate the interior angle of a regular octagon.
Can a regular octagon tessellate the plane by itself? Explain why or why not.
Describe how Escher used tessellations in his artwork.
Describe the process for creating a tessellation using a translation transformation.
Describe the role of symmetry in tessellations.
Explain the difference between a regular and a semi-regular tessellation.
Explain why a regular pentagon cannot tessellate the plane by itself.
Explain why the sum of the angles at a vertex in a tessellation must be exactly 360°.
Given a regular hexagon, how many such hexagons meet at a point in a regular tessellation?
Given a regular polygon with n sides, what is the formula for its interior angle?
If the sum of the angles at a vertex in a tessellation is not 360°, what will happen?
Name the three types of regular tessellations.
A student claims that any convex polygon can tessellate the plane. Is this statement true or false? Justify your answer.
A tessellation is created using only regular dodecagons (12-sided polygons). Determine whether this tessellation is possible and justify your answer mathematically.
Consider a tessellation where each vertex is surrounded by two squares and three equilateral triangles. Write the vertex configuration notation for this tessellation.
Given a tessellation formed by regular hexagons and equilateral triangles, calculate the number of each type of polygon that meet at a single vertex if the arrangement is 3.6.3.6.
Prove that a regular polygon with n sides can tessellate the plane by itself if and only if (n - 2) × 180° / n is a divisor of 360°.
