Draw the given 3D shapes to scale using isometric paper.

Problem Description:

The task is to draw the given 3D shapes on isometric dot paper. The goal is to represent these shapes in a scaled manner using the isometric grid, which helps in visualizing 3D objects in a 2D format.

Shapes to Draw:

1. Cube with side length 3 cm
2. Rectangular prism with dimensions 6 cm × 3 cm × 2 cm
3. Irregular 3D shape with base dimensions 5 cm × 5 cm and height 4 cm, with a smaller cube of side 1 cm protruding from one corner

Solution Explanation:

#### Step 1: Understanding Isometric Dot Paper
Isometric dot paper consists of dots arranged in a triangular grid pattern. Each dot represents a point in 3D space, and lines connecting these dots represent edges of 3D shapes. In isometric drawing:
- The x-axis, y-axis, and z-axis are drawn at 120° angles to each other.
- Each unit on the grid represents a fixed length (e.g., 1 cm).

#### Step 2: Drawing the Cube (3 cm × 3 cm × 3 cm)
1. Base: Start by drawing a square on the isometric grid. Each side of the square should be 3 units long (since each unit represents 1 cm).
- Place the first dot as the starting point.
- Move 3 units along the x-axis (rightward diagonal).
- Move 3 units along the y-axis (leftward diagonal).
- Close the square by moving back to the starting point.
2. Height: From each corner of the base square, draw vertical lines upward (parallel to the z-axis) for 3 units.
3. Top Face: Connect the top ends of these vertical lines to form another square parallel to the base.

#### Step 3: Drawing the Rectangular Prism (6 cm × 3 cm × 2 cm)
1. Base: Draw a rectangle on the isometric grid with dimensions 6 cm × 3 cm.
- Start with a dot as the origin.
- Move 6 units along the x-axis (rightward diagonal) for the longer side.
- Move 3 units along the y-axis (leftward diagonal) for the shorter side.
- Complete the rectangle by connecting the dots.
2. Height: From each corner of the base rectangle, draw vertical lines upward (parallel to the z-axis) for 2 units.
3. Top Face: Connect the top ends of these vertical lines to form a rectangle parallel to the base.

#### Step 4: Drawing the Irregular 3D Shape
1. Base: Draw a square on the isometric grid with dimensions 5 cm × 5 cm.
- Start with a dot as the origin.
- Move 5 units along the x-axis (rightward diagonal).
- Move 5 units along the y-axis (leftward diagonal).
- Complete the square by connecting the dots.
2. Height: From each corner of the base square, draw vertical lines upward (parallel to the z-axis) for 4 units.
3. Protrusion: At one corner of the base square, add a smaller cube of side 1 cm.
- From the chosen corner, draw a smaller square (1 cm × 1 cm) on the base.
- Extend vertical lines upward from this smaller square for 4 units.
- Connect the top ends to form the smaller cube.

Final Answer:

The shapes are drawn as follows:
1. Cube: A perfect cube with all sides equal to 3 cm.
2. Rectangular Prism: A rectangular prism with dimensions 6 cm × 3 cm × 2 cm.
3. Irregular Shape: A larger square base (5 cm × 5 cm) with a height of 4 cm, and a smaller cube (1 cm × 1 cm × 4 cm) protruding from one corner.

Final Answer:
\[
\boxed{\text{Draw the shapes as described above on isometric dot paper.}}
\]