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Exploring Polygons Worksheet

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Exploring Polygons Worksheet

A polygon is a closed, flat shape made only from straight line segments. Work through the clues, show your calculations and use a ruler where needed.

Spot the sides and names

Use the number of straight sides to classify each shape.

1.A badge has 8 straight sides. What is the name of this polygon?
2.Match each side count to its polygon name.
  • 3 sides
  • 5 sides
  • 6 sides
  • 10 sides
  • Decagon
  • Triangle
  • Pentagon
  • Hexagon
3.Which statement must be true of a regular polygon?
  • It has at least 5 sides.
  • All its sides are equal, and all its interior angles are equal.
  • It has exactly one pair of parallel sides.
  • All its sides are different lengths.
4.A closed shape is made from 6 straight line segments. Is it a polygon? Explain briefly.

Angle detectives

For a polygon with n sides, the sum of its interior angles can be found by dividing it into triangles from one vertex.

5.Choose the correct rule for finding the sum of the interior angles of an n-sided polygon.
  • n × 180°
  • (n − 2) × 180°
  • (n + 2) × 180°
  • n × 360°
6.A regular pentagon is divided into 3 triangles from one vertex. Use this to find the sum of its interior angles. Show your calculation.
7.A heptagon has 7 sides. Calculate the sum of its interior angles and show your working.
8.The interior angles of a polygon add to 1,440°. How many sides does it have? Show how you know.

Make and explain

Use the drawing space to build a polygon of your own.

9.Draw a regular hexagon. Mark all six vertices, then write the size of each interior angle. (The interior angles of a regular polygon are equal.)
10.A regular polygon has 9 sides. What is its name, and what is the size of each interior angle? Show your calculation.
11.Harry says, “Every polygon with equal sides is regular.” Is she correct? Explain using the definition of a regular polygon.

3 printable pages

  • Exploring Polygons Worksheet, page 1 of 3: Spot the sides and names

    Page 1

  • Exploring Polygons Worksheet, page 2 of 3: Angle detectives, Make and explain

    Page 2

  • Exploring Polygons Worksheet, page 3 of 3: 10. A regular polygon has 9 sides. What is its name, and what is the size of each…

    Page 3

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