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

Example

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

P = 5 · 6 = 30 cm

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.

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