3D Shapes Worksheet for Classifying and Counting Faces

Let’s go step by step to fill in the table for each 3D shape. We’ll count how many of each type of face (triangular, rectangular, hexagonal, octagonal) each shape has.

Remember:
- A face is a flat surface on a 3D shape.
- We’re only counting faces that are triangles, rectangles, hexagons, or octagons — not squares unless they’re counted as rectangles (but note: the cube example says “Number of rectangular faces = 6” and “Number of square faces = 0”, so here “rectangular” means non-square rectangles? Wait — actually, looking at the cube: it has 6 square faces, but the table says “Number of rectangular faces = 6” and “Number of square faces = 0”. That seems odd… unless they consider squares as a type of rectangle? But then why separate them?

Wait — let’s look again at the cube row:

Cube:
- Shape Picture: cube
- Number of triangular faces: 0 → correct
- Number of rectangular faces: 6 → but cubes have square faces, not rectangular (unless they mean “rectangle including squares”)
- Number of hexagonal faces: 0 → correct
- Number of octagonal faces: 0 → correct

But then it says “Number of square faces = 0” — which is wrong if we think normally. So maybe there’s a mistake in the example? Or perhaps the column “Number of rectangular faces (including squares)” is meant to include squares, and then “Number of square faces” is redundant? But in the cube row, it says 6 rectangular (including squares) and 0 square faces — that doesn’t make sense.

Wait — re-read the column header:
“Number of rectangular faces (including squares)” — so this column counts both rectangles AND squares. Then there’s a separate column “Number of square faces”.

But in the cube example, it says:
- Rectangular faces (including squares): 6 → that’s correct, since all 6 faces are squares, and squares are rectangles.
- Square faces: 0 → that must be a typo! It should be 6.

But the problem says: “Look carefully at some 3D shapes and fill in the spaces...” and gives the cube row already filled. So maybe we have to follow their logic even if it seems off? Or perhaps I misread.

Looking back at the image description:
In the cube row, under “Number of square faces” it says 0. But that can’t be right. Unless... wait, maybe the column “Number of square faces” is only for shapes that have square faces that are NOT part of the rectangular count? No, that doesn’t make sense.

Alternatively, perhaps the “Number of square faces” column is meant to be used when a shape has square faces that are distinct from other rectangular faces — but for a cube, all faces are squares, so it should be 6.

I think there might be an error in the provided example. But since this is a worksheet given to students, and the cube row is pre-filled, we should assume that for the purpose of this task, “rectangular faces (including squares)” means any four-sided face with right angles (so squares are included), and “square faces” is a separate count — but in the cube, they put 0 for square faces, which is confusing.

Wait — let me check the original user input again. The user wrote:

> Cube | [picture] | 0 | 6 | 0 | 0

And the columns are:
- Shape Name
- Shape Picture
- Number of triangular faces
- Number of rectangular faces (including squares)
- Number of hexagonal faces
- Number of octagonal faces

There is NO “Number of square faces” column! In my initial reading, I thought there was, but looking back:

The columns are:
1. Shape Name
2. Shape Picture
3. Number of triangular faces
4. Number of rectangular faces (including squares)
5. Number of hexagonal faces
6. Number of octagonal faces

Ah! I made a mistake earlier. There is no “Number of square faces” column. The fourth column is “Number of rectangular faces (including squares)”, meaning it includes both rectangles and squares. So for a cube, all 6 faces are squares, which are a type of rectangle, so it’s correct to say 6 rectangular faces (including squares). And there are no triangular, hexagonal, or octagonal faces, so those are 0.

Okay, that makes sense now. So we don’t have a separate “square faces” column — it’s all under “rectangular faces (including squares)”.

So let’s proceed correctly.

We need to fill for:

1. Cuboid
2. Triangular prism
3. Hexagonal prism
4. Octagonal prism
5. Square based pyramid
6. Tetrahedron
7. Octahedron

Let’s take them one by one.

---

Cuboid:

A cuboid is like a box — all faces are rectangles (or sometimes squares, but generally rectangles). It has 6 faces, all quadrilaterals with right angles. None are triangles, hexagons, or octagons.

So:
- Triangular faces: 0
- Rectangular faces (including squares): 6 (since all 6 are rectangles; if any are squares, they’re still included here)
- Hexagonal faces: 0
- Octagonal faces: 0

---

Triangular prism:

This has two triangular bases and three rectangular sides.

So:
- Triangular faces: 2 (the two ends)
- Rectangular faces: 3 (the sides connecting the triangles)
- Hexagonal: 0
- Octagonal: 0

---

Hexagonal prism:

Two hexagonal bases and six rectangular sides.

So:
- Triangular: 0
- Rectangular: 6
- Hexagonal: 2 (the two bases)
- Octagonal: 0

---

Octagonal prism:

Two octagonal bases and eight rectangular sides.

So:
- Triangular: 0
- Rectangular: 8
- Hexagonal: 0
- Octagonal: 2

---

Square based pyramid:

One square base and four triangular faces meeting at the top.

So:
- Triangular faces: 4
- Rectangular faces: 0? Wait — the base is a square, which is a rectangle. So according to the column “rectangular faces (including squares)”, the square base counts as 1 rectangular face.

Is that correct? Yes, because the column says “including squares”.

So:
- Triangular: 4
- Rectangular (including squares): 1 (the square base)
- Hexagonal: 0
- Octagonal: 0

---

Tetrahedron:

This is a pyramid with a triangular base — so all four faces are triangles.

So:
- Triangular: 4
- Rectangular: 0
- Hexagonal: 0
- Octagonal: 0

---

Octahedron:

This is a Platonic solid with 8 triangular faces. Think of two square pyramids stuck together at the base.

All faces are triangles.

So:
- Triangular: 8
- Rectangular: 0
- Hexagonal: 0
- Octagonal: 0

---

Now let’s summarize:

| Shape Name | Triangular Faces | Rectangular Faces (incl. squares) | Hexagonal Faces | Octagonal Faces |
|---------------------|------------------|-----------------------------------|-----------------|-----------------|
| Cube | 0 | 6 | 0 | 0 |
| Cuboid | 0 | 6 | 0 | 0 |
| Triangular prism | 2 | 3 | 0 | 0 |
| Hexagonal prism | 0 | 6 | 2 | 0 |
| Octagonal prism | 0 | 8 | 0 | 2 |
| Square based pyramid| 4 | 1 | 0 | 0 |
| Tetrahedron | 4 | 0 | 0 | 0 |
| Octahedron | 8 | 0 | 0 | 0 |

Double-checking:

- Cuboid: yes, 6 rectangular faces.
- Triangular prism: 2 triangles + 3 rectangles → correct.
- Hexagonal prism: 2 hexagons + 6 rectangles → correct.
- Octagonal prism: 2 octagons + 8 rectangles → correct.
- Square pyramid: 4 triangles + 1 square (counted as rectangular) → correct.
- Tetrahedron: 4 triangles → correct.
- Octahedron: 8 triangles → correct.

All good.

Final Answer:

For the table:

- Cuboid: Triangular=0, Rectangular=6, Hexagonal=0, Octagonal=0
- Triangular prism: Triangular=2, Rectangular=3, Hexagonal=0, Octagonal=0
- Hexagonal prism: Triangular=0, Rectangular=6, Hexagonal=2, Octagonal=0
- Octagonal prism: Triangular=0, Rectangular=8, Hexagonal=0, Octagonal=2
- Square based pyramid: Triangular=4, Rectangular=1, Hexagonal=0, Octagonal=0
- Tetrahedron: Triangular=4, Rectangular=0, Hexagonal=0, Octagonal=0
- Octahedron: Triangular=8, Rectangular=0, Hexagonal=0, Octagonal=0