## hexagon

### A hexagon is a polygon with six sides and six angles

A hexagon is a polygon with six sides and six angles. The name “hexagon” is derived from the Greek words “hexa” meaning six and “gonia” meaning angles.

Properties of a regular hexagon:

1. All six sides of a regular hexagon are of equal length.

2. All six angles of a regular hexagon are of equal measure and each angle measures 120 degrees.

3. Opposite sides of a regular hexagon are parallel.

Classification of hexagons:

1. Regular hexagon: All sides and angles are equal.

2. Irregular hexagon: Sides and/or angles are not equal.

3. Convex hexagon: All interior angles are less than 180 degrees.

4. Concave hexagon: At least one interior angle is greater than 180 degrees.

Formulas related to hexagons:

1. Perimeter: The perimeter of a hexagon can be found by multiplying the length of one side by six.

Perimeter = Length of one side × 6

2. Area: The area of a hexagon can be calculated using various formulas depending on the given information, such as side length or apothem (the perpendicular distance from the center to a side).

– If the side length (s) is known, the formula is:

Area = (3√3 × s^2) / 2

– If the apothem (a) is known, the formula is:

Area = (3 × a × s) / 2

– If the radius (r) of the circumscribed circle is known, the formula is:

Area = (3√3 × r^2)/2

In summary, a hexagon is a six-sided polygon with various properties and classifications. It has multiple formulas to calculate perimeter and area depending on the given information about the sides, apothem, or radius.

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