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 this volume, we need to use the formula that includes the area of the hexagonal base and the height of the prism.
Answer
Volume = \frac{3\sqrt{3}}{2} a^2 \times h
Answer for screen readers
Therefore, the volume of the hexagonal prism is given by the formula: $$ V = \frac{3\sqrt{3}}{2} a^2 \times h $$
Steps to Solve
To find the volume of a hexagonal prism, follow these steps:
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Calculate the area of the hexagonal base A regular hexagon can be divided into 6 equilateral triangles. The formula for the area of an equilateral triangle with side length $ a $ is: $$ A_{ ext{triangle}} = \frac{\sqrt{3}}{4} a^2 $$ Therefore, the area of the hexagonal base is: $$ A_{ ext{hexagon}} = 6 \times \frac{\sqrt{3}}{4} a^2 = \frac{3\sqrt{3}}{2} a^2 $$
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Multiply the area of the hexagon by the height of the prism If the height of the prism is $ h $, then the volume $ V $ is given by: $$ V = A_{ ext{hexagon}} \times h = \frac{3\sqrt{3}}{2} a^2 \times h $$
Therefore, the volume of the hexagonal prism is given by the formula: $$ V = \frac{3\sqrt{3}}{2} a^2 \times h $$
More Information
Hexagonal prisms are often found in natural structures, such as basalt columns and the molecular structures of some crystals.
Tips
Common mistakes include forgetting to square the side length of the hexagon or using the incorrect height measurement for the prism.
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