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 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)

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

Properties

a regular pentagon
made of 3 triangles

A regular pentagon has:

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

Any pentagon has:

• Sum of Interior Angles of 540°
• 5 diagonals

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):

Make a "pretzel" knot with the paper.

Carefully tighten the knot while keeping the paper flat.

.....

Trim off (or fold back) any excess.

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

Images

This Petunia is almost a perfect pentagon

The "Pentagon" in Washington DC
is 5 regular pentagons with a common center.

Masterclass

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