91Ó°ÊÓ

A solid prism, like the one in this example, often has a base shape that is a rectangle. The base of a prism is crucial because it directly influences the calculation of its volume.
In our example, the bottom face of the prism is defined by the four vertices

• (0,0,0)
• (4,0,0)
• (4,6,0)
• (0,6,0)

These coordinates outline a perfect rectangle that lies flat on the plane where z = 0.
With the given length of 4 units and width of 6 units, the rectangular base is both simple and illustrative of the principles of geometry. Knowing the dimensions of the base rectangle is the starting point for further calculations.

Understanding 3D geometry is essential when working with shapes like prisms. In this context, we deal with axes: x, y, and z.
These axes allow us to position shapes in a three-dimensional space. Vertices describe points where edges meet, providing a blueprint of the prism's shape.
In the given problem, additional vertices such as (0,0,1) and (4,0,1) represent the top edges of the prism. This indicates a vertical height that extends the flat rectangle into a 3D prism.
Thus, geometry helps us visualize how the rectangle we see in 2D transforms into a 3D shape with volume.

Calculating the volume of a prism combines knowledge of geometry with mathematical formulas. The key to finding volume is to multiply the area of its base by its height.
The base area has already been determined to be 24 square units, as the product of its length and width i.e., \( 4 \times 6 \).
The height of the prism, in our example, is easy to identify. It is the distance between the two planes of the prism, here being simply 1 unit.
The formula for determining the volume of a prism is: \[ \text{Volume} = \text{Base Area} \times \text{Height} \]
By substituting the known values, we can conclude that the prism's volume is \( 24 \times 1 = 24 \) cubic units.
Understanding each step ensures clear comprehension and accuracy in solving similar volume calculation problems.