Skip to content
MathAnvil
§ Geometry·Grades 5–7

Polygon Properties Worksheets

Free PDF · Problems + answer key · Instant download

Easy

10 problems

Medium

20 problems

Hard

20 problems

Mixed

30 problems

Free printable polygon properties worksheets with step-by-step answer keys. Every worksheet is uniquely generated so students never see the same problems twice. Topics covered range from count sides/corners of named polygons at the easy level through to exterior angle / sides / diagonals of a regular polygon at the advanced level.

CCSS.5.GCCSS.7.G

What is polygon properties?

A polygon is a closed figure formed by three or more straight line segments called sides, which meet at points called vertices. Each polygon is classified by its number of sides: a triangle has 3 sides, a quadrilateral has 4 sides, a pentagon has 5 sides, and so on. Regular polygons have all sides equal in length and all angles equal in measure.

Why it matters

Polygon properties appear throughout architecture, engineering, and design. Stop signs use regular octagons because their 8 equal sides create visual balance and recognition from any angle. Soccer balls combine pentagons and hexagons — each pentagon is surrounded by 5 hexagons, creating the familiar spherical shape through 32 total faces. In computer graphics, complex curved surfaces are approximated using thousands of triangular polygons. The interior angle formula (n-2)×180°/n determines how polygon tiles fit together: regular hexagons tessellate perfectly because each 120° interior angle allows exactly 3 hexagons to meet at each vertex (3×120° = 360°). Understanding these relationships prepares students for trigonometry, coordinate geometry, and calculus, where polygon approximations help calculate areas under curves.

Common mistakes to watch for

  • ✗Confusing interior and exterior angles leads to calculating 360°÷6 = 60° for a hexagon's interior angle instead of the correct (6-2)×180°÷6 = 120°.
  • ✗Mixing up the formulas results in using (n-2)×180° for a single interior angle rather than the sum of all interior angles, giving 720° for one hexagon angle instead of 120°.
  • ✗Forgetting that exterior angles sum to 360° for any polygon causes errors like claiming a pentagon's exterior angles sum to 540° instead of 360°.

Questions teachers ask

What is the difference between regular and irregular polygons?+
Regular polygons have all sides equal in length and all angles equal in measure, like a square or regular hexagon. Irregular polygons have sides or angles that differ in size, such as a rectangle (equal angles but unequal sides) or a scalene triangle (unequal sides and angles).
How do you find the number of sides from an interior angle?+
Use the formula n = 360°÷(180° - interior angle). For example, if each interior angle measures 144°, then n = 360°÷(180° - 144°) = 360°÷36° = 10 sides, making it a decagon. This works only for regular polygons.
Why do exterior angles always sum to 360°?+
Walking around any polygon's perimeter means turning through one complete rotation, which equals 360°. Each exterior angle represents the amount of turning at each vertex. Regardless of the polygon's shape or number of sides, the total turning remains one full circle.
What happens to polygon angles as the number of sides increases?+
Interior angles approach 180° while exterior angles approach 0° as sides increase. A triangle has 60° interior angles, a hexagon has 120°, and a 100-sided polygon has 176.4° interior angles. This is why circles appear to have 180° interior angles everywhere.
How are polygon names determined by their sides?+
Polygon names combine Greek or Latin number prefixes with '-gon' meaning angle. Triangle (3), quadrilateral (4), pentagon (5), hexagon (6), heptagon (7), octagon (8), nonagon (9), decagon (10), and dodecagon (12) are the most common. Beyond 12 sides, polygons are often called n-gons.
Generate worksheet →Free · No account · Unlimited

Pick a difficulty

Click any level to open the generator with that difficulty pre-selected.

Beginner

Generate →
Concepts
Count sides/corners of named polygons
Range
3–12 sides
Steps
1 step
Example
How many sides does a hexagon have?

Easy

Generate →
Concepts
Name polygon from number of sides
Range
3–12 sides
Steps
1 step
Example
What is a 7-sided polygon called?

Medium

Generate →
Concepts
Interior angles of a regular polygon ((n−2)·180/n)
Range
3–12 sides
Steps
1 step
Example
Interior angle of a regular hexagon?

Hard

Generate →
Concepts
Exterior angle / sides / diagonals of a regular polygon
Range
5–12 sides
Steps
1 step
Example
Exterior angle of a regular octagon?

Try a sample problem

Try it right now

Click “Generate a problem” to see a fresh example of this technique.

Learn the theory → Read our polygon properties guide with worked examples.

Practice online → Interactive polygon properties problems with instant feedback.