Tessellation Worksheets - Free Printable

To determine if a shape can tessellate, we need to see if we can copy it and arrange the copies together to cover a flat surface without any gaps or overlaps.

Here is the step-by-step check for each shape:

a. Parallelogram:
If you take a parallelogram and slide copies of it next to each other, they fit perfectly side-by-side. You can stack rows of them on top of each other, and they will fill the space completely.
* Result: yes

b. Circle:
If you place circles next to each other, there will always be curved empty spaces (gaps) between them because their edges are round. They cannot lock together tightly.
* Result: no

c. Star:
This is a standard five-pointed star. If you try to push two of these stars together, the points of one star will hit the inner corners of the other, leaving large diamond-shaped gaps that cannot be filled by another identical star.
* Result: no

d. Hourglass (Two triangles joined at a point):
Imagine flipping this shape upside down. The wide top of the upright shape fits perfectly into the wide bottom of the upside-down shape. By alternating upright and upside-down shapes, they lock together like puzzle pieces with no gaps.
* Result: yes

e. Arrow / Chevron:
This shape has an indentation on one side and a point on the other. The point of one arrow fits perfectly into the indentation of the next arrow. You can line them up in a row, and then stack another row on top (flipped or shifted) to fill the plane.
* Result: yes

f. Rounded Rectangle:
Similar to the circle, this shape has curved corners. When you place them next to each other, the curves prevent the corners from touching fully, leaving small gaps between the shapes. Only shapes with straight edges and specific angles can usually tessellate perfectly without gaps.
* Result: no

g. Zig-zag Lightning Bolt:
This shape is essentially a slanted parallelogram that has been cut and shifted. Because the "steps" on the left match the "steps" on the right, and the top matches the bottom, you can slide these shapes together. The indentations of one piece accept the protrusions of another, creating a solid pattern.
* Result: yes

h. Shape with one curved side:
This shape has three straight sides and one curved side. While the straight sides might match up with others, the single curved side creates a problem. You cannot fit another identical shape against that curve without leaving a gap or overlapping, because the matching "bump" needed to fill the "dent" isn't present on the opposite side in a way that allows for a repeating grid.
* Result: no

i. T-Shape:
This is a classic tessellating shape. You can fit the "arms" of one T into the empty space under the arms of another T. By rotating some Ts 180 degrees (upside down), they interlock perfectly to cover the entire area.
* Result: yes

Final Answer:
a. yes
b. no
c. no
d. yes
e. yes
f. no
g. yes
h. no
i. yes