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05.12 • Polygons

Pentagon

Use side count to name pentagon accurately, then connect that five-sided structure to its interior-angle and diagonal patterns.

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⬠ Pentagon
Interactive diagram

Pentagon Diagram

Keep the boundary closed and count the five sides carefully before discussing whether the figure is regular or irregular.

Use the movable diagram to see what defines pentagon, how the labels relate to the figure, and what stays true as the board changes.

Definition: A pentagon is a polygon with five sides.
Detailed definition

Understanding Pentagon

Pentagon is a polygon with five sides. A pentagon is a polygon with five sides. The same shape can be regular or irregular, convex or concave, but it remains a pentagon as long as the side count is five.

A regular pentagon has strong symmetry and a fixed interior angle of one hundred eight degrees at each vertex. In a general pentagon, the angle measures may vary, but the total interior angle sum remains five hundred forty degrees.

Pentagons are useful because they introduce side-count naming while also showing that naming and regularity are separate ideas. You name the polygon first and then describe whether it is regular or irregular.

Key facts

Important ideas to remember

  • A pentagon is a polygon with five sides.
  • A pentagon always has five sides and five vertices.
  • The interior angle sum of any pentagon is five hundred forty degrees.
  • A regular pentagon has five equal sides and five equal interior angles of one hundred eight degrees.
Where it is used

Where pentagon shows up

  • Use pentagon naming when classifying polygons by side count.
  • Use regular-pentagon facts in angle and symmetry problems.
  • Use pentagons as examples when introducing general polygon formulas.
Common mistakes

What to watch out for

  • Do not confuse five sides with five angles as separate counts; a pentagon has both because it has five vertices.
  • Do not treat regular pentagon facts as though they apply to every pentagon.
  • Do not miscount the boundary when the polygon is concave or irregular.
Worked examples

Pentagon examples

Use these worked examples to see the idea in a clean diagram first, then in the kind of reasoning students usually need for classwork, homework, or test practice.

Example 1

Example 1: Naming a pentagon from its side count

Count the sides and vertices carefully so the polygon name comes from the correct total.

  • Start at one vertex and count around the boundary once.
  • Match the count to the standard polygon name.
  • Check that the shape closes after the final side.

Result: The polygon is named accurately because the side count and vocabulary agree.

Example 2

Example 2: Connecting pentagon to its regular form

Use the same side count to discuss the regular version of the polygon without changing the name itself.

  • Keep the side count fixed.
  • Notice how equal sides and equal angles change the look of the figure.
  • Separate the naming rule from the regularity rule.

Result: The student can name the polygon first and then discuss whether it is regular or irregular.

For

Why this page helps

This page helps because pentagon is one of the first named polygons beyond quadrilaterals. It gives students a clean bridge from familiar shapes to broader n-gon thinking.

Do

What you can do here

  • Count the five sides and compare regular and irregular pentagon cases.
  • See how the side count stays fixed while the angle pattern changes.
  • Download a clean pentagon diagram for naming or angle-sum review.
Learning outcome

What this page helps you do

These takeaways are meant to help you recognize the idea faster, read diagrams more accurately, and use the topic with more confidence in real problems.

1

Pentagon

Name five-sided polygons more confidently.

2

Pentagon

Separate side-count identity from regularity facts.

3

Pentagon

Build a stronger bridge from special shapes to general polygon logic.

05

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An irregular polygon does not have all sides and angles equal.

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A hexagon is a polygon with six sides.

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