Printable 3D shapes worksheet for learning about prisms and pyramids.

Problem Overview:

The worksheet focuses on identifying and understanding 3D shapes, specifically prisms and pyramids. The tasks involve naming the shapes, identifying their properties (such as faces, edges, and vertices), and determining cross-sections of prisms.

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Solution and Explanation:

#### 1. Naming Prisms and Pyramids
We need to identify each shape as either a prism or a pyramid and name them based on their base shapes.

- Top Row:
1. Triangular Pyramid: The base is a triangle.
2. Hexagonal Prism: The base is a hexagon.
3. Rectangular Prism: The base is a rectangle.
4. Triangular Pyramid: The base is a triangle.

- Second Row:
1. Pentagonal Prism: The base is a pentagon.
2. Tetrahedron (Triangular Pyramid): All faces are triangles.
3. Triangular Pyramid: The base is a triangle.
4. Hexagonal Prism: The base is a hexagon.

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#### 2. Properties of Prisms
We need to determine the cross-sections of the given prisms when cut along the dotted lines.

- First Column:
- Cube: Cutting along the red line results in a square.
- Triangular Prism: Cutting along the red line results in a triangle.
- Rectangular Prism: Cutting along the red line results in a rectangle.

- Second Column:
- Hexagonal Prism: Cutting along the red line results in a hexagon.
- Triangular Prism: Cutting along the red line results in a triangle.
- Rectangular Prism: Cutting along the red line results in a rectangle.

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#### 3. Properties of Pyramids
We need to name the shape of the base and label the apex (top vertex) of each pyramid.

- First Row:
1. Square Pyramid: Base is a square.
2. Triangular Pyramid: Base is a triangle.

- Second Row:
1. Triangular Pyramid: Base is a triangle.
2. Square Pyramid: Base is a square.

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#### 4. Properties of Prisms and Pyramids
We need to count the number of faces, edges, and vertices for each shape.

- Square Pyramid:
- Faces: 5 (1 square base + 4 triangular faces)
- Edges: 8 (4 base edges + 4 slant edges)
- Vertices: 5 (4 base vertices + 1 apex)

- Triangular Prism:
- Faces: 5 (2 triangular bases + 3 rectangular lateral faces)
- Edges: 9 (3 base edges × 2 + 3 connecting edges)
- Vertices: 6 (3 base vertices × 2)

- Triangular Pyramid:
- Faces: 4 (1 triangular base + 3 triangular faces)
- Edges: 6 (3 base edges + 3 slant edges)
- Vertices: 4 (3 base vertices + 1 apex)

- Hexagonal Prism:
- Faces: 8 (2 hexagonal bases + 6 rectangular lateral faces)
- Edges: 18 (6 base edges × 2 + 6 connecting edges)
- Vertices: 12 (6 base vertices × 2)

- Rectangular Prism:
- Faces: 6 (2 rectangular bases + 4 rectangular lateral faces)
- Edges: 12 (4 base edges × 2 + 4 connecting edges)
- Vertices: 8 (4 base vertices × 2)

- Triangular Prism:
- Faces: 5 (2 triangular bases + 3 rectangular lateral faces)
- Edges: 9 (3 base edges × 2 + 3 connecting edges)
- Vertices: 6 (3 base vertices × 2)

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Final Answer:

\[
\boxed{
\text{
1. Naming Prisms and Pyramids: Triangular Pyramid, Hexagonal Prism, Rectangular Prism, Triangular Pyramid, Pentagonal Prism, Tetrahedron, Triangular Pyramid, Hexagonal Prism.
2. Properties of Prisms: Square, Triangle, Rectangle, Hexagon, Triangle, Rectangle.
3. Properties of Pyramids: Square Pyramid, Triangular Pyramid, Triangular Pyramid, Square Pyramid.
4. Properties of Prisms and Pyramids: See detailed counts above.
}}
\]