Regular and irregular polygons · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Regular and irregular polygons

Mathematics · Geometry · ages 9-10
Name ______________________   Date ____________

  1. A regular pentagon has all sides equal. How many equal angles does it have?

    Answer: ______________

  2. Which shape is a regular polygon?

    • An equilateral triangle
    • A rectangle that is not a square
    • A kite
    • An isosceles triangle

  3. A polygon has 5 equal sides and 5 equal angles. Is it regular or irregular?

    • Regular
    • Irregular
    • Not a polygon

  4. A regular pentagon has 5 equal sides and 5 equal angles.

    Circle one:   True   False

  5. A square has 4 equal sides. How many equal sides do two squares have in total?

    Answer: ______________

  6. A regular pentagon has how many equal sides?

    Answer: ______________

  7. A regular hexagon has 6 equal sides. What else is true about it?

    • All 6 angles are equal
    • It has 5 sides
    • Two sides are longer
    • One angle is 90 degrees

  8. Nora says a regular pentagon has 5 equal angles. Is Nora right?

    Circle one:   True   False

  9. Milo says a shape is regular whenever all its angles are equal. Priya says he also needs to check the sides. Who is right?

    • Milo, because angles are enough
    • Priya, because both sides and angles must be equal
    • Neither, because regular polygons don't have angles

  10. The angles of a regular pentagon add to 540 degrees. What is each angle?

    Answer: ______________

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Regular and irregular polygons W1-mt_8H2kO4k2B9-s1

  1. 5 · A regular pentagon has 5 equal angles.
  2. An equilateral triangle · An equilateral triangle has equal sides and equal angles.
  3. Regular · Every side and every angle matches, so it fits the definition of regular.
  4. True · That is exactly what makes a pentagon regular: matching sides and matching angles.
  5. 8 · 2 x 4 = 8 equal sides.
  6. 5 · Regular means every side matches, and a pentagon has 5 sides in total.
  7. All 6 angles are equal · Regular hexagons have 6 equal angles too.
  8. True · Nora is right: regular pentagons match on all 5 corners.
  9. Priya, because both sides and angles must be equal · Equal angles alone are not enough. A rectangle's angles match but its sides don't, so it stays irregular unless it's a square.
  10. 108 · 540 divided by 5 is 108 degrees.
Worksheet · LightMySky