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Exploring the characteristics and volume calculations of prisms, this content delves into the geometry of prisms, including their types and the formulas for determining their volume. It highlights the practical applications of these calculations in various fields such as architecture and product design, and explains how to compute the volume of composite prismatic shapes for real-life problem-solving.

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## Definition of Prisms

### Polyhedron with congruent and parallel faces

Prisms are three-dimensional shapes with two identical and parallel faces

### Lateral faces and bases

Parallelogram-shaped lateral faces

The lateral faces of a prism are parallelograms formed by connecting the corresponding vertices of the bases

Classification based on shape of base

Prisms are classified based on the shape of their base, such as triangular, square, rectangular, pentagonal, or hexagonal

### Orientation of prisms

The orientation of a prism, whether it is right or oblique, does not change its defining properties

## Volume Calculations

### Formula for calculating volume

The volume of a prism is calculated by multiplying the area of its base by its height

### Determining base area

Varying base area by type of prism

The area of a prism's base is determined by its shape, such as the product of length and width for a rectangular base or 1/2 times the base length times the height for a triangular base

Multiplying base area by prism height

After calculating the base area, it is multiplied by the prism's height to find the volume

### Volume formulas for different types of prisms

Rectangular prism

The volume of a rectangular prism is found by multiplying its length, width, and height

Triangular prism

The volume of a triangular prism is calculated by taking 1/2 times the base length times the height of the triangle and multiplying by the prism's height

Cube

The volume of a cube is s^3, where s is the side length

Trapezoidal prism

The volume of a trapezoidal prism is found by multiplying the average of the lengths of the two parallel sides by the height of the trapezium and the prism's height

Regular hexagonal prism

The volume of a regular hexagonal prism is calculated by multiplying the area of the hexagon by the prism's height

### Practical applications of prism volume calculations

Calculating the volume of prisms is useful in determining storage capacity and required construction materials

### Decomposing complex structures into simpler prisms

Complex structures can be broken down into simpler prisms to calculate their aggregate volume

### Expressing volume in different units of measure

The volume of prisms can be expressed in various units, such as cubic meters or liters, to determine their capacity

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