Vidaara.orgClass 8 · Mathematics
CodeVID-M08-12-RGT-01
Regular Polygons & Tessellations - Assignment
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
5 × 1 = 5 marks
1.
A regular polygon has equal sides and equal:
- A.diagonals
- B.angles
- C.areas
- D.vertices
2.
A tessellation covers a plane with:
- A.gaps
- B.overlaps
- C.no gaps or overlaps
- D.curves
3.
Which does NOT tessellate?
- A.equilateral triangle
- B.square
- C.regular hexagon
- D.regular pentagon
4.
At a tessellation vertex, the angles sum to:
- A.$180^\circ$
- B.$270^\circ$
- C.$360^\circ$
- D.$90^\circ$
5.
A regular polygon that tessellates is the:
- A.pentagon
- B.square
- C.heptagon
- D.nonagon
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Does a square tessellate?
7.
Does a regular pentagon tessellate?
8.
The angles at a tessellation point sum to:
9.
Name a regular polygon that tessellates.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
How many equilateral triangles meet at a point in a tessellation?
11.
How many squares meet at a tessellation point?
12.
How many regular hexagons meet at a point?
13.
Why does a regular pentagon not tessellate?
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Explain, using interior angles, why squares tessellate but regular pentagons do not.
15.
Show how many regular hexagons meet at a vertex in a tessellation and verify the angle sum.
Answer Key
Section A — Multiple Choice Questions
- (B) angles
- (C) no gaps or overlaps
- (D) regular pentagon
- (C) $360^\circ$
- (B) square
Section B — Short Answer (2 marks)
- Yes.
- No.
- $360^\circ$.
- Triangle (or square / hexagon).
Section C — Short Answer (3 marks)
- $6$ ($6\times60^\circ=360^\circ$).
- $4$ ($4\times90^\circ=360^\circ$).
- $3$ ($3\times120^\circ=360^\circ$).
- Its interior angle $108^\circ$ does not divide $360^\circ$ evenly.
Section D — Long Answer (5 marks)
- A square's interior angle $90^\circ$ divides $360^\circ$ (four meet at a point); a pentagon's $108^\circ$ does not divide $360^\circ$, leaving gaps.
- $3$ hexagons; $3\times120^\circ=360^\circ$.
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