Q1
A pattern of shapes covering a surface without gaps is called a:
Atessellation
Breflection
Crotation
Ddilation
CBSEClass 7 (CBSE)MathematicsCh 14 · Topic 2
Tiling Patterns (Tessellations)
Exploring how shapes can tile a plane without gaps or overlaps.
Core concept
For a shape to tessellate on its own, the interior angle must divide evenly into 360° (the total angle around any point) — a square's 90° angle fits exactly 4 times (4×90°=360°), a hexagon's 120° angle fits exactly 3 times (3×120°=360°), but a regular pentagon's 108° angle does not divide evenly into 360°, explaining why pentagons alone cannot tessellate a plane without gaps. Tessellations appear in nature (honeycomb patterns), art (Islamic geometric designs, M.C. Escher's artwork), and practical applications like floor and wall tiling.
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• A tessellation covers a surface completely with shapes, without gaps or overlaps.
• Squares, equilateral triangles, and regular hexagons can each tessellate a plane alone.
• A shape tessellates alone if its interior angle divides evenly into 360°.
• Tessellations appear in nature (honeycombs), art (Escher), and tiling.