Goals
1. Understand the definition and properties of a regular hexagon.
2. Learn the formula for calculating the area of a regular hexagon.
3. Apply knowledge of area calculation to practical problems.
Contextualization
Hexagons are really interesting geometric shapes that show up often in nature, like the honeycombs made by bees, as well as in various human designs, such as floor patterns and tiles. Knowing how to calculate the area of a hexagon is super important, not just for tackling mathematical problems, but also for applying this understanding in fields like architecture, engineering, and interior design. For example, when working on a hexagon-shaped room, it's essential to know how to calculate the area to figure out how much flooring you'll need.
Subject Relevance
To Remember!
Definition of Hexagon and Regular Hexagon
A hexagon is a polygon with six sides and six angles. A regular hexagon is a special type of hexagon where all sides and angles are equal. This symmetry makes the regular hexagon a geometric figure that is incredibly interesting in both theoretical mathematics and practical applications.
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A hexagon has six sides and six angles.
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In a regular hexagon, all sides and angles are equal.
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The symmetry of the regular hexagon simplifies the calculation of area and other geometric properties.
Properties of Hexagons
Hexagons have quite a few interesting properties. For instance, the sum of the internal angles of a hexagon always adds up to 720 degrees. In a regular hexagon, each internal angle measures 120 degrees. What's more, regular hexagons can be split into six equilateral triangles, making the area calculation easier.
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The sum of the internal angles of a hexagon is 720 degrees.
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Each internal angle of a regular hexagon measures 120 degrees.
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Regular hexagons can be divided into six equilateral triangles.
Formula for Calculating the Area of a Regular Hexagon
To calculate the area of a regular hexagon, we use the formula: Area = (3 * square root of 3 * side²) / 2. This formula comes from adding up the areas of the six equilateral triangles that create the regular hexagon. Knowing this formula helps solve real-life problems when determining hexagonal areas.
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The area formula is: Area = (3 * square root of 3 * side²) / 2.
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This formula comes from summing the areas of six equilateral triangles.
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Using this formula makes it easier to solve practical problems involving hexagons.
Practical Applications
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In architecture, hexagons are often used in the design of floor patterns and roofs due to their spatial efficiency.
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In engineering, hexagonal structures are common in construction materials because of their strength and effective use of resources.
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In nature, bee honeycombs are hexagonal, allowing for effective space and material use.
Key Terms
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Hexagon: A polygon with six sides and six angles.
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Regular Hexagon: A hexagon where all sides and angles are equal.
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Area of Regular Hexagon: (3 * square root of 3 * side²) / 2.
Questions for Reflections
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How can knowledge of hexagons be applied in your future profession?
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What other geometric shapes do you believe are important to understand apart from hexagons?
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How can you use the efficiency of space in hexagons in your daily life?
Practical Challenge: Building and Calculating a Hexagon
In this mini-challenge, you will create a physical model of a regular hexagon using basic materials and calculate its area. This hands-on activity will solidify your understanding of hexagon geometry and its applications.
Instructions
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Divide into groups of 4-5 students.
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Draw and cut out a regular hexagon with a side length of 10 cm using cardboard or paper.
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Measure the apothem of the hexagon, which is the line from the centre to the midpoint of one side.
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Using the area formula for a regular hexagon (Area = (3 * square root of 3 * side²) / 2), calculate the area of your hexagon.
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Each group should present their hexagon and explain the steps they took to calculate the area.
