A pentagon is a polygon with five sides and five vertices.
A regular pentagon is a polygon with five equal sides and angles.
Angles of the Pentagon
The sum of interior angles of a pentagon = (5 − 2) · 180° = 540°
The value of an interior angle of a regular pentagon is: 540º : 5 = 108º
The central angle of a regular pentagon measures: 360º : 5 = 72º
Diagonals of the Pentagon
The number of diagonals in a regular pentagon = 5 · (5 − 3) : 2 = 5
Apothem of the Regular Pentagon
By applying the Pythagorean theorem for one of the triangles, we obtain:
Perimeter of a Regular Pentagon
Perimeter = 5 · l
Area of a Regular Pentagon
Calculate the apothem, perimeter and area of a regular pentagon with a side of 6 cm.
P = 5 · 6 = 30 cm