Composing and decomposing 2D shapes worksheets - Free Printable

To solve the missing parts of this worksheet, we need to look at how the shapes are put together (composed) in the examples above them.

Step 1: Solve Box 11 (Bottom Left)
* Look at the pieces: The image shows 4 triangles. Specifically, they look like small equilateral triangles arranged in a row.
* Find a matching example: Look at the right-hand column, fourth row down. It shows that 6 triangles make a hexagon. This tells us the hexagon is made of 6 equal triangular slices.
* Analyze the shape: If you take a hexagon and remove two of those triangular slices from opposite sides, or simply arrange 4 of these triangles point-to-point or side-by-side, what do you get?
* Let's look at another clue. In the left column, second row, 4 triangles make a square. However, the triangles in box 11 are oriented differently than the ones in the square example.
* Let's look at the arrangement in box 11. It looks like a strip. But wait, let's look at the purple shapes again.
* Left column, 4th row: 2 triangles make a rhombus.
* Box 11 has 4 triangles. If you put two rhombuses together, or 4 triangles, you can often make a larger rhombus, a parallelogram, or a trapezoid.
* Let's look closely at the specific triangles in box 11. They are arranged in a zig-zag line. This specific arrangement of 4 equilateral triangles creates a long parallelogram (specifically, a rhombus if the angles were different, but here it's elongated).
* *Correction/Refinement:* Let's look at standard tangram or pattern block logic.
* 2 triangles = Rhombus.
* 3 triangles = Trapezoid (see right column, bottom example which is incomplete, but 3 triangles usually make a trapezoid in these sets).
* 4 triangles = A larger Rhombus (if arranged in a 2x2 grid) or a Parallelogram (if arranged in a strip). The image in box 11 shows them in a strip/zig-zag. This shape is a parallelogram.
* *Alternative interpretation:* Is it a Trapezoid? No, a trapezoid is usually 3 triangles.
* Is it a Hexagon? No, that's 6.
* Let's look at the purple shape in the right column, 4th row. It's a hexagon made of 6 triangles.
* Let's look at the purple shape in the left column, 4th row. It's a rhombus made of 2 triangles.
* Box 11 has 4 triangles. If you combine two rhombuses (which are each 2 triangles), you get a larger shape. The arrangement shown (zig-zag) forms a parallelogram.

* *Let's re-evaluate based on common elementary geometry sets:*
* Often, "4 triangles" in these specific visual puzzles refers to forming a larger triangle (if arranged in a pyramid) or a parallelogram. The shape drawn is clearly a parallelogram.

* *Wait, let's look at Box 12 first, it might be easier.*

Step 2: Solve Box 12 (Bottom Right)
* Look at the pieces: The image shows 3 triangles. One is pointing up, and two are pointing down/sideways attached to it.
* Visualize the combination: If you take one central triangle and attach two more to its sides, you create a three-sided figure with a flat top.
* Identify the shape: A four-sided shape with one pair of parallel sides is a trapezoid. In pattern blocks, 3 equilateral triangles always form a trapezoid.

Step 3: Re-evaluating Box 11
* Now that we know Box 12 is likely a trapezoid (3 triangles), let's look at Box 11 (4 triangles) again.
* The shape formed by the 4 triangles in the drawing is an elongated quadrilateral.
* In many of these worksheets, the answer key for "4 triangles" arranged in that specific zig-zag way is a parallelogram.
* However, sometimes 4 triangles are used to make a larger triangle (with a hole in the middle? No, that's decomposition).
* Let's check the previous purple example: 2 triangles = Rhombus.
* If you put two rhombuses together, you get a parallelogram.
* Therefore, the shape in Box 11 is a parallelogram.

Summary of Answers:
* Box 11: The 4 triangles form a parallelogram.
* Box 12: The 3 triangles form a trapezoid.

Final Answer:
11: parallelogram
12: trapezoid