Regular Pentagons

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

Diagonals of a Regular Pentagon

Apothem of the Regular Pentagon

Apothem of a Regular Pentagon


By applying the Pythagorean theorem for one of the triangles, we obtain:

Perimeter of a Regular Pentagon

Perimeter = 5 · l

Regular Pentagon

Area of a Regular Pentagon

Area of a Regular Pentagon Formula


Example

Calculate the apothem, perimeter and area of a regular pentagon with a side of 6 cm.

Regular Pentagon

Pentagon Operations

Pentagon Operations

P = 5 · 6 = 30 cm

Pentagon Solution