Class 7 Tiling Patterns — practice questions with answers
Geometry · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. Covering a flat surface with copies of shapes so that there are no gaps and no overlaps is called:
Asymmetry
Btiling
Crotation
Dconstruction
Show answer
Answer: B) tiling
When shapes cover a surface completely, with no gaps and no overlaps, we say they tile the surface. The pattern is called a tiling (or tessellation).
2. A regular polygon can tile on its own only if its angle divides 360° exactly. Which angle passes this test?
A120°
B108°
C140°
D135°
Show answer
Answer: A) 120°
360 ÷ 120 = 3 ✓. 360 ÷ 108, 360 ÷ 135 and 360 ÷ 140 are not whole numbers.
3. Which tangram piece has the same area as the two small triangles put together?
AA large triangle
BThe whole tangram
CThe square
DOne small triangle
Show answer
Answer: C) The square
Each small triangle is 1 unit, so two of them make 2 units. The square is also 2 units (so are the medium triangle and the parallelogram). A large triangle is 4 units.
4. Square tiles have each been cut along both diagonals into four triangles, as shown. How many 45° angles meet at the marked corner point?
A4
B2
C6
D8
Show answer
Answer: D) 8
Each of the 4 squares around the point gives two 45° angles there (one from each triangle on either side of the diagonal). 8 × 45° = 360° ✓.
5. On an 8 × 8 chessboard, the two opposite corner squares (both white) are removed. Why can't 2 × 1 tiles cover the 62 squares that remain?
A62 is an odd number
BEach tile covers 1 black and 1 white, but 32 black and 30 white remain
CCorner squares are needed to start
DAn 8 × 8 board cannot be tiled at all
Show answer
Answer: B) Each tile covers 1 black and 1 white, but 32 black and 30 white remain
Any 2 × 1 tile on a chessboard covers one black and one white square. 31 tiles would need 31 black and 31 white, but 32 black and only 30 white are left. (62 is even, so counting alone does not settle it.)