Prism and pyramid worksheet - Free Printable

The image you provided appears to be a worksheet featuring various 3D geometric shapes. The task seems to involve identifying or classifying these shapes based on their properties. Below, I will analyze the shapes and provide explanations for each.

Step-by-Step Analysis of the Shapes

#### Row 1:
1. Shape 1: This is a rectangular prism (or cuboid). It has six faces, all of which are rectangles. Opposite faces are congruent.
2. Shape 2: This is a cube. It is a special type of rectangular prism where all six faces are squares, and all edges are of equal length.
3. Shape 3: This is another rectangular prism (cuboid), similar to Shape 1. The orientation might differ, but it still has six rectangular faces.

#### Row 2:
4. Shape 4: This is a tetrahedron. It is a polyhedron with four triangular faces, six edges, and four vertices. All faces are equilateral triangles in a regular tetrahedron.
5. Shape 5: This is a hexagonal prism. It has two hexagonal bases and six rectangular lateral faces. The bases are parallel and congruent.
6. Shape 6: This is another tetrahedron, similar to Shape 4. It also has four triangular faces.

#### Row 3:
7. Shape 7: This is an octahedron. It is a polyhedron with eight triangular faces, twelve edges, and six vertices. In a regular octahedron, all faces are equilateral triangles.
8. Shape 8: This is a rectangular prism (cuboid) with one face shaded blue. Like the other prisms, it has six rectangular faces.
9. Shape 9: This is a pentagonal pyramid. It has a pentagonal base and five triangular faces that meet at a single vertex (apex).

Summary of Shapes:

1. Rectangular prism (cuboid)
2. Cube
3. Rectangular prism (cuboid)
4. Tetrahedron
5. Hexagonal prism
6. Tetrahedron
7. Octahedron
8. Rectangular prism (cuboid)
9. Pentagonal pyramid

Solution Explanation:

The task likely involves identifying or labeling each shape based on its geometric properties. Here’s how you can approach it:
- Prisms: Identify shapes with two parallel and congruent bases connected by rectangular or parallelogram-shaped lateral faces.
- Pyramids: Identify shapes with a polygonal base and triangular faces that meet at a single apex.
- Regular Polyhedra: Identify shapes like the cube, tetrahedron, and octahedron, which have uniform faces and symmetry.

Final Answer:

The shapes are classified as follows:
1. Rectangular prism
2. Cube
3. Rectangular prism
4. Tetrahedron
5. Hexagonal prism
6. Tetrahedron
7. Octahedron
8. Rectangular prism
9. Pentagonal pyramid

$$
\boxed{\text{Rectangular prism, Cube, Rectangular prism, Tetrahedron, Hexagonal prism, Tetrahedron, Octahedron, Rectangular prism, Pentagonal pyramid}}
$$