Composing and Decomposing Shapes

In geometry, we can play with shapes just like building blocks! We can put them together to make new shapes, or we can break big shapes apart into smaller ones. Let's learn how this works.

What is Composing Shapes?

Composing means putting things together. When we compose shapes, we take two or more smaller shapes and combine them to build a brand new, bigger shape.

Examples of Composing:

• If you take two identical triangles and put their longest sides together, you can make a square or a rectangle.
• If you put two squares side-by-side, you create a longer rectangle.
• Six small triangles can be put together in a circle to make a hexagon.

What is Decomposing Shapes?

Decomposing means breaking things apart. When we decompose a shape, we take one big shape and split it into smaller shapes.

Examples of Decomposing:

• Imagine a rectangle. If you draw a straight line right down the middle, you decompose it into two smaller squares or two smaller rectangles.
• If you draw a diagonal line from one corner of a square to the opposite corner, you decompose the square into two triangles.

Let's Practice!

Here are some fun ways to think about composing and decomposing shapes:

1. "What shapes make up this figure?" Look at a simple drawing of a house. You might see that it is composed of a triangle (the roof) and a square (the main building).

2. "Combine $2$ triangles to make a new shape." If you grab two paper triangles and move them around, what can you build? Depending on how you line them up, you could make a bigger triangle, a square, or a diamond (rhombus)!

3. "How many squares can you see in this figure?" Sometimes a big square is decomposed into $4$ smaller squares. If you count the $4$ small ones inside and the $1$ big one on the outside, you have $5$ squares in total!

Understanding how to compose and decompose shapes helps us see the hidden geometry in the world all around us!