Pentagon (EP)

A pentagon is a polygon with five sides and five angles. The name "pentagon" is derived from the Greek words "pente" (πέντε) meaning "five" and "gonia" (γωνία) meaning "angle."

Types of Pentagons:

• Regular Pentagon: A regular pentagon has five equal sides and five equal angles (each measuring 108 degrees). It possesses five lines of reflectional symmetry and rotational symmetry of order 5.

• Irregular Pentagon: An irregular pentagon has sides and angles that are not all equal.

• Convex Pentagon: A convex pentagon has all its interior angles less than 180 degrees. A line segment connecting any two points inside the pentagon lies entirely within the pentagon.

• Concave Pentagon: A concave pentagon has at least one interior angle greater than 180 degrees. A line segment connecting two points inside the pentagon may lie partially outside the pentagon.

Properties of Pentagons:

• The sum of the interior angles of any pentagon is 540 degrees.
• A regular pentagon can be inscribed in a circle, meaning all its vertices lie on the circle's circumference.
• The area of a regular pentagon with side length 's' can be calculated using the formula: Area = (1/4) * sqrt(25 + 10 * sqrt(5)) * s^2

Occurrences:

Pentagons appear in various contexts, including:

• Architecture: The Pentagon, the headquarters of the United States Department of Defense, is a famous building with a pentagonal shape.
• Geometry: Pentagons are fundamental geometric shapes studied in mathematics.
• Nature: Some flowers and starfish exhibit pentagonal symmetry.
• Design: Pentagons are used in various designs, such as tiles and patterns.