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Polygon Decomposition Practice

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Polygon Decomposition Practice

A toy designer is planning new polygon tiles. Decompose means to break a shape into parts by drawing straight lines. Complete each puzzle. When you draw, make your lines meet the shape’s vertices where asked.

Spot the Pieces

Help the designer identify the shapes made by each cut.

1.A pentagon is split into a triangle and a quadrilateral. How many sides do the two new shapes have altogether?
  • 5 sides
  • 7 sides
  • 8 sides
  • 9 sides
2.A hexagon tile is divided into parts with straight sides. Which of these could be one of the pieces? Select all that apply.
  • Triangle
  • Rectangle
  • Circle
  • Pentagon
3.Complete the idea: To decompose a polygon is to break it into .

Draw the Cuts

Imagine each outline as a flat tile. Draw straight lines to make the requested pieces.

4.Draw one straight line from one corner of a rectangle to the opposite corner. What two shapes does your cut make?
5.Draw one line inside a pentagon to split it into a triangle and a quadrilateral. Then name both pieces.
6.A polygon has six sides. Draw lines from one vertex to the other non-adjacent vertices to decompose it into triangles. How many triangles do you make?

Explain Your Strategy

Use what you know about sides, corners, and straight lines to solve the final puzzles.

7.True or false: If you draw a diagonal between opposite corners of a rectangle, you make two triangles.
TrueFalse
8.Aaliyah says, “A polygon can only be decomposed into triangles.” Is Aaliyah correct? Explain your answer with one example.
9.A quadrilateral has two pairs of opposite corners. How many different diagonals can you draw to split it into two triangles? Draw them and explain.

3 printable pages

  • Polygon Decomposition Practice, page 1 of 3: Spot the Pieces, Draw the Cuts

    Page 1

  • Polygon Decomposition Practice, page 2 of 3: Explain Your Strategy

    Page 2

  • Polygon Decomposition Practice, page 3 of 3: 9. A quadrilateral has two pairs of opposite corners. How many different diagonals

    Page 3

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