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Calculating volume is an essential part of understanding geometry and helps us understand the space that a 3-dimensional object occupies. To find the volume of a shape, you typically need to know two main components: a base area and a height. These components vary depending on the type of geometric figure. In this case of a prism, the volume formula is straightforward, where the key is to multiply the area of the base by the height of the prism. This formula is versatile because once you have the area of the base, you only need the height to complete the calculation.

Remember, volume is measured in cubic units, reflecting the three-dimensional space the object fills. Here, both the base area and height are given in centimeters, making the resulting volume 120 cm³.

Prisms are fascinating shapes formed by two parallel, congruent bases. The most common prisms include rectangular, triangular, and hexagonal, like the one we're discussing. Regardless of the base shape, the volume of any prism can be calculated using the formula:

• \( V = B \times h \)

Where:

• \( V \) is the volume of the prism.
• \( B \) is the area of the prism's base.
• \( h \) is the height or the perpendicular distance between the two bases.

Thanks to the consistent shape of prisms, this single formula applies universally. Once you understand this formula, finding the volume of any prism becomes a task of plugging in the base area and height into the equation.

A hexagonal prism is a type of polyhedron with two hexagonal bases and rectangular lateral faces. These shapes are unique because they combine characteristics of both hexagons and rectangular prisms. Each hexagonal base connects six rectangular faces, forming a symmetrical shape with various practical applications in architecture and packaging.

The volume formula for a hexagonal prism remains \( V = B \times h \), where the base \( B \) is calculated as the area of a hexagon. In geometric terms, if you know the side length \( s \) of the regular hexagon, its area can be calculated using:
\[ \text{Area of hexagon} = \frac{3\sqrt{3}}{2}s^2 \]

In our exercise, the base area is already given as \(12 \ ext{cm}^2\), but knowing this formula lets you understand how we arrive at base area measurements for hexagonal prisms.

Mathematical problem solving is an essential skill that involves understanding the problem, applying formulas correctly, and performing calculations efficiently. In the context of the given exercise, this involves several key steps:

• Understanding the geometric shape involved: a hexagonal prism.
• Identifying the correct volume formula to use, which reflects the prism's structure.
• Substituting known values into the formula, ensuring units are consistent.
• Executing calculations accurately to obtain the volume.

Good problem solving often entails cross-verifying calculations and ensuring that logic flows step-by-step. It's about building confidence through practice, gaining familiarity with the formulas, and developing the habit of checking work meticulously. These skills not only improve mathematical understanding but also bolster logical thinking skills applicable in various real-world scenarios.