Pentagon

A pentagon is a 5-sided Polygon (a flat shape with straight sides):

Regular or Irregular

When all angles are equal and all sides are equal it is regular, otherwise it is irregular:

Regular Pentagon Irregular PentagonIrregular Pentagon
Regular Pentagon Irregular Pentagons

Concave or Convex

A convex pentagon has no angles pointing inwards. More precisely, no internal angles can be more than 180°.

When any internal angle is greater than 180° it is concave. (Think: concave has a "cave" in it)

Irregular Pentagon Irregular Pentagon
Convex Pentagon Concave Pentagon

Is it a Pentagon?

A pentagon has 5 straight sides. The shape must also be closed (all the lines connect up):

Pentagon Not a Pentagon Not a Pentagon
Pentagon
(straight sides)
Not a Pentagon
(has a curve)
Not a Pentagon
(open, not closed)

Properties

A regular pentagon has:

  • Interior Angles of 108°
  • Exterior Angles of 72°
  • Area of approximately 1.7204774 × s2 (where s=side length)

Make a Regular Pentagon

You can make a regular pentagon with a strip of paper!

Start with a long strip of paper, make sure it is the same width all along (if you want the pentagon to be regular):

Strip oif Paper

Make a "pretzel" knot with the paper.

Pretzel knot

Carefully tighten the knot while keeping the paper flat.

Pretzel knot ..... Pretzel knot

Trim off (or fold back) any excess.

Pretzel knot

All sides are now of equal length, and all angles should be the same too.

Masterclass

How to construct a Pentagon using just a compass and a straightedge.