Tessellations

Math ⇒ Geometry

Tessellations starts at 7 and continues till grade 12. QuestionsToday has an evolving set of questions to continuously challenge students so that their knowledge grows in Tessellations. How you perform is determined by your score and the time you take. When you play a quiz, your answers are evaluated in concept instead of actual words and definitions used.

See sample questions for grade 12

Calculate the interior angle of a regular octagon and determine if it can tessellate the plane by itself.

Calculate the number of regular polygons that can tessellate the plane by themselves.

Describe a real-world application of tessellations.

Describe the process for determining if a regular polygon can tessellate the plane.

Describe the role of symmetry in tessellations.

Explain the difference between a regular tessellation and a semi-regular tessellation.

Explain the term 'vertex configuration' in the context of tessellations.

Explain why regular pentagons cannot tessellate the plane by themselves.

Explain why the sum of the angles at a vertex in a tessellation must be 360°.

Given a tessellation made from regular octagons and squares, what type of tessellation is this?

Given a tessellation pattern where each vertex is surrounded by two squares and three equilateral triangles, what is the vertex configuration?

If a tessellation uses only congruent rectangles, what type of tessellation is it?

Name all regular polygons that can tessellate the plane by themselves.

A tessellation is created using only regular hexagons and equilateral triangles. Determine the vertex configuration and prove whether this tessellation is semi-regular.

Consider a tessellation where each vertex is surrounded by two regular hexagons and one regular dodecagon. Calculate the sum of the interior angles at each vertex and determine if such a tessellation is possible.

Explain the difference between a periodic and an aperiodic tessellation, and provide an example of each.

Given a context: A designer wants to create a tessellation using only regular polygons where each vertex is surrounded by one square, one regular hexagon, and one regular dodecagon. Is this tessellation possible? Justify your answer mathematically.

Prove that any convex quadrilateral can tessellate the plane, and explain the process by which this tessellation can be constructed.

Prove that the sum of the reciprocals of the number of sides of regular polygons that can tessellate the plane by themselves is equal to 1/2.