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Questions and Answers
What is the sum of the interior angles of a hexagon?
What is the formula for the area of a regular hexagon?
What is a characteristic of an irregular hexagon?
What is a concave hexagon?
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What is an example of a complex hexagon?
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What is the meaning of the Greek root word 'gonia' in the term 'hexagon'?
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What is a common property of the sides of a regular hexagon?
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What is the sum of the lengths of the sides of a two-dimensional body called?
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What is the measure of each interior angle of a regular hexagon?
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What is the term for a two-dimensional, closed geometrical shape made up of straight line segments?
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Study Notes
Definition of a Hexagon
- A hexagon is a two-dimensional shape with six sides and six interior angles.
- The term "hexagon" comes from Greek roots "hex" meaning "six" and "gonia" meaning "corner".
Features of a Hexagon
- A hexagon is a polygon, a two-dimensional, closed geometrical shape made up of straight line segments.
- It has six equal sides and angles, making it a regular polygon.
Regular Hexagons
- A regular hexagon has six equal line segments making six equal angles.
- All sides and angles of a regular hexagon are equal in dimension.
- The perimeter of a regular hexagon is the sum of all its sides.
- Each interior angle of a regular hexagon measures 120 degrees.
- A regular hexagon is equiangular, meaning all angles have equal measure.
Angles of a Regular Hexagon
- A regular hexagon can be thought of as consisting of six identical equilateral triangles.
- Each angle of a regular hexagon has two angles of an equilateral triangle, each measuring 60 degrees.
Formula for the Area of a Regular Hexagon
- The formula for the area of a regular hexagon is (3 * sqrt(3) * a^2) / 2, where a is the side length of the hexagon.
- Another formula for the area of a regular hexagon is (3 * (a^2 * sqrt(3)) / 4), where a is the side of the hexagon and d is the height of the hexagon from one of the bases.
Irregular Hexagons
- An irregular hexagon is one that does not have six equal sides and six equal angles.
- Not all sides and angles of an irregular hexagon have to have different measures.
Features of Irregular Hexagons
- All interior angles of an irregular hexagon do not measure 120 degrees.
- All exterior angles of an irregular hexagon do not measure 60 degrees.
- The perimeter of an irregular hexagon is not given by a simple formula, but rather by adding individual side lengths.
Convex Irregular Hexagons
- A convex hexagon is a hexagon with an outward curved design, where all interior angles are less than 180 degrees.
Concave Irregular Hexagons
- A concave hexagon is a hexagon with one or more surfaces curved inwards, where at least one interior angle is greater than 180 degrees.
Complex Hexagons
- Complex hexagons are six-sided, closed structures formed by the intersection of different shapes, such as the Star of David.
Hexagons in Nature
- Hexagons exist naturally in the formation of snowflakes, the crystalline structure of graphene, and in the honeycombs made by bees.
- Hexagonal rocks can sometimes occur naturally, and the center scutes on a turtle's carapace are also hexagonal in shape.
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Description
Learn about the definition, features, and properties of hexagons, including their sides, angles, and regular polygon properties.
