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Polygon Classification

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Polygon Classification

Help plan a new garden for a community space in Aotearoa New Zealand. Classify the polygon-shaped garden beds and explain how you know. A polygon is a closed shape made only from straight line segments.

Polygon check-in

Use the information in each question to answer Questions 1–3.

1.Mere sketches a closed shape with five straight sides. What is the shape called?

Pentagon
Hexagon
Octagon
Dodecagon

2.A regular polygon has all sides the same length and all interior angles the same size. Select every statement that must be true of a regular hexagon.

It has six straight sides.
It has six vertices.
All six sides are equal in length.
At least one side is curved.
All six interior angles are equal.

3.A garden-bed outline has four sides: three are straight and one is curved. Is the outline a polygon? Explain why or why not.

Sort the garden beds

Use the written descriptions of Outlines A–C to classify each by its number of sides, then decide whether it is regular or irregular.

Outline A: A closed triangle with three equal sides and three equal angles.

Outline B: A closed square with four equal sides and four equal angles.

Outline C: A closed, simple, non-crossing pentagon with five straight sides of unequal lengths.

4.Outline D is a closed shape with 6 straight sides. Match its name to the number of sides.

Hexagon
Octagon
Dodecagon
Quadrilateral

5.Rangi draws a heptagon with seven sides. How many vertices does it have?

6.A student says, “Every quadrilateral is a square.” Is this true or false? Give one reason for your answer.

TrueFalse

Design and explain

Show that you can classify polygons using their properties.

7.Draw an irregular hexagon for a new garden bed. Make it a closed shape with six straight sides, and label its six vertices. Then explain what makes it irregular.

8.A regular octagon has 8 sides. How many vertices does it have, and what two properties make it regular?

9.Challenge: Hana is choosing between a regular pentagon and an irregular pentagon for a sign. Both have five sides. What extra information would tell her which one is regular?