Calculate the volume of the L-shaped prism.

The image shows an L-shaped prism with dimensions indicated by numbers. To calculate the volume, we can decompose the prism into simpler rectangular prisms or use the concept of subtraction of volumes if it were a cutout from a larger prism. Since the dimensions are given, we can treat it as a composite shape of rectangular prisms.

Let's assume the prism can be divided into two rectangular blocks. There are a few ways to do this. One common way is to divide it horizontally or vertically.

Method 1: Dividing into two horizontal blocks

• Block 1 (Top): Dimensions are 7 (length) x 3 (width) x 2 (height). Volume = 7 * 3 * 2 = 42 cubic units.
• Block 2 (Bottom): The remaining part has a length of 4 (width). The height of this block is 8 - 2 = 6. The depth of this block can be inferred from the other side. If we consider the total width of the bottom part as 4, and the top part's width as 3, then the protruding part of the bottom block has a width of 4 - 3 = 1, but this is not directly given or implied easily. Let's re-evaluate the decomposition. Let's consider the bottom part has a width of 4. The height is 8. The length needs to be determined. If we consider the shape from the front, it looks like a rectangle of 8x4 with a smaller rectangle removed from the top right. This interpretation is also difficult without more clarity.

Let's reconsider the decomposition from the given numbers.

Method 2: Dividing into two vertical blocks

• Imagine the shape split vertically.
• Left Block: Dimensions are 4 (width) x 8 (height) x Depth. The depth is not explicitly given for the entire shape. However, we have a 3 on one side and a 7 on the other side for the lengths. This suggests the depth might be consistent across the entire shape. Let's assume the depth of the prism is consistent and can be inferred. From the top view, it looks like a larger rectangle with a smaller rectangle removed. The dimensions 7 and 3 seem to be along the length. The dimension 4 seems to be along the width at the bottom. The dimension 8 is along the height. The dimensions 3 and 2 are also given for the upper part.

Let's assume the dimensions are as follows, considering the standard interpretation of such diagrams:

• The front-left vertical edge is 8.
• The bottom front edge is 4.
• The bottom left edge is some depth (let's call it D).
• The top horizontal edge of the longer part is 7.
• The vertical edge between the longer and shorter top parts is 2.
• The horizontal edge of the shorter top part is 3.
• The width of the shorter top part is 3.

This is still ambiguous. Let's try to interpret the diagram as a standard L-shape extruded. Assume the base is the 'L' shape on the XY plane, and the height is along the Z-axis.

Let's assume the 'depth' of the prism is consistent, and let's denote it by 'd'. From the labeling, we can infer the dimensions of the 'L' shape in one plane (e.g., top view or front view) and then extrude it.

Looking at the numbers:

• Height = 8
• Bottom width = 4
• Top longer length = 7
• Top shorter length = 3
• The vertical step in the top section = 2. This means the height of the lower part of the top section is 8 - 2 = 6.
• The width of the side part is 3.

It seems the shape is defined in 3 dimensions. Let's try to break it down into rectangular prisms based on the numbers provided.

Consider the shape as a large rectangular prism with a smaller rectangular prism removed from a corner. This is not the case here; it's an 'L' shape.

Let's assume the base is the 'L' shape on the floor, and the height is 8.

Method 3: Decomposing into three rectangular prisms

Let's assume the