Pentagon Side Length

This Side Length of a Pentagon from Area calculator computes the length of sides required to have an area of a regular pentagon with 5 equal sides.

INSTRUCTIONS: Choose units and enter the following:

• (A) Area of Pentagon

Side Length (s): The length is returned in meters.  However, this can be automatically converted to compatible units via the pull-down menu.

The Math / Science

A regular pentagon has five equal sides and equal angles.  The formula for the area of a regular pentagon is as follows:

`A = 5/4 * sqrt( 1 + 2/ sqrt(5))* s^2`

where:

• A = Area of the Pentagon
• s = Length of the sides

Solving for s, we get the following formula for the side length of a regular pentagon:

`s = sqrt(A / [ 5/4 * sqrt(1 + 2/sqrt(5))] ) `

Pentagon Information

A pentagon is a polygon with five sides and five angles. It is a two-dimensional geometric shape formed by connecting five straight line segments (sides) in a closed loop. Each interior angle of a regular pentagon (where all sides and angles are equal) measures 108 degrees. The sum of the interior angles in any pentagon is 540 degrees.

Pentagons can come in various forms, and their sides and angles may have different lengths and measures. Regular pentagons are often encountered in geometry and design, and they have a symmetrical and balanced appearance. In practical terms, pentagons might be found in certain architectural elements, decorative patterns, and various other contexts.

Pentagon Calculators

• Pentagon Area: Regular pentagon area from side length.
• Irregular Pentagon Area: Area from sides and diagonals.
• Pentagon Side Length: Side length of regular pentagon from area.
• Pentagon Volume: Volume of regular pentagon column.
• Pentagon Planter: Soil volume and planting surface area of a pentagon shaped raised planter.
• Water in a Pentagon Pond: Water to fill a pentagon (regular) shaped pond at depth.
• Dodecahedron Surface Area: Surface area of regular dodecahedron based on side length.
• Dodecahedron Volume: Volume of regular dodecahedron based on side length.

In three dimensions, twelve (12) regular pentagons can be fused to form a dodecahedron.  A dodecahedron is a three-dimensional geometric shape characterized by having 12 flat faces, 20 vertices (corners), and 30 edges. Each face is a regular pentagon.  Dodecahedra can be found in various natural and man-made forms. In geometry, they are studied for their interesting properties and symmetrical characteristics. In certain games and puzzles, dodecahedra may also be used as components or shapes.

Regular Polygon Information

A regular polygon is a geometric shape with three or more straight sides where every side is the same length and every angle between connecting sides are the same angle. Because of the symmetry of the regular polygon, all the vertices of the polygon can be constructed to touch a circle in which the regular polygon is inscribed and all the chords that are polygon sides will then obviously be of equal length .  Likewise, because of the regular polygon's symmetry, a circle constructed to be inscribed in a regular polygon and touching the polygon will touch the regular polygon at the midpoint of the polygon side.  As shown in the pictures, Figure 1 and Figure 2, lines from the regular polygon's vertices to the circle's center form n isosceles triangles of equal area.

The names of polygons vary based on the number of sides as follows:

• triangle - 3 sides
• square - 4 sides 
• pentagon - 5 sides
• hexagon - 6 sides
• heptagon - 7 sides
• octagon - 8 sides
• nonagon - 9 sides
• decagon - 10 sides
• hendecagon - 11 sides
• dodecagon - 12 sides

Common Regular Polygon Functions

Polygon Area Calculators:

• Polygon Area from the Number of sides and Length of Sides
• Polygon Area from the Number of Sides and Outside Radius
• Area of a Polygon Segment (triangle) from the Number of Sides and Inscribed Radius
• Polygon Area from the Number of Sides and Inscribed Radius.

Polygon Side Calculators

• Length of a Polygon Side from the Number of Sides and Outer Radius
• Length of a Polygon Side from the Number of Sides and Inner Radius
• Length of a Polygon Side from the Number of Sides and Area in Poloygon

Polygon Perimeter Calculators

• Perimeter of a Polygon from Number of Sides and Length of Sides
• Perimeter of a Polygon from Number of Sides and Outer Radius
• Perimeter of a Polygon from Number of Sides and Inner Radius
• Polygon Perimeter from the Area and Number of Sides

Polygon Radius

• Radius of Circle around a Polygon

3D Polygon Shapes

• Polygon Ring Volume

Other Polygon Calculators

• Interior Angle of a Regular Polygon based on the number of sides
• Area of Circle - Circle approximates a polygon as the number of sides approaches infinity.
• Area of Triangle -  Three Sides
• Area of a Square - Four Sides
• Area of Pentagon - Five Sides
• Area of Hexagon - Six Sides
• Area of Heptagon - Seven Sides
• Area of Octagon - Eight Sides
• Area of Nonagon - Nine Sides
• Area of Decagon - Ten Sides
• Area of Hendecagon - Eleven Sides
• Area of Dodecagon - Twelve Sides