How to find the volume of a hexagonal prism?
Understand the Problem
The question is asking for the method to calculate the volume of a hexagonal prism. To find the volume, we will use the formula that involves the area of the hexagonal base and the height of the prism.
Answer
\frac{3\sqrt{3}}{2} a^2 h
Answer for screen readers
V = \frac{3\sqrt{3}}{2} a^2 h
Steps to Solve
- Find the area of the hexagonal base
The formula for the area of a regular hexagon with side length $a$ is: $$ ext{Area} = \frac{3\sqrt{3}}{2} a^2$$
- Identify the height of the prism
Let $h$ be the height of the prism. This is the perpendicular distance between the two hexagonal bases.
- Calculate the volume
Using the area of the base and the height, the volume $V$ of a hexagonal prism is given by the formula: $$V = ext{Area of base} \times ext{Height} = \frac{3\sqrt{3}}{2} a^2 h$$
V = \frac{3\sqrt{3}}{2} a^2 h
More Information
The hexagonal shape is quite common in nature, including in the honeycombs made by bees.
Tips
A common mistake is to confuse the side length $a$ with another measure like the length of a diagonal. Be careful to use the correct measurement for $a$.
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