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Shape-classification algorithms

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Required skills (click to reveal)

A school is ordering geometry teaching materials and needs to sort 34 identical regular hexagons and 16 identical isosceles right-angled triangles for classroom use. Using a flow chart algorithm that first checks the number of sides, then checks for equal sides and angles, classify the shapes.

The algorithm proceeds as follows: (1) If the shape has 3 sides, classify as a triangle. (2) If the shape has 4 or more sides, check if all sides are equal and all angles are equal. (3) If yes, classify as a regular polygon. (4) If not, classify as irregular. What fraction of the total shapes (34 hexagons and 16 triangles) are classified as regular polygons?

Answer as a simplified fraction in the form a/b.

Concept illustrations

These are separate worked examples of related concepts, not a diagram of this question. Their values and dimensions do not describe your question.

Classifying from known properties. For a quadrilateral already known to have four right angles, check whether all four sides are equal. Yes gives a square; no gives a rectangle that is not a square. A square remains a rectangle too.4 right anglesRectangle→4 equal sides?Check lengths→Yes: squareNo: non-square
For a quadrilateral already known to have four right angles, check whether all four sides are equal. Yes gives a square; no gives a rectangle that is not a square. A square remains a rectangle too.
Squares belong to two broader families. A square is both a rectangle and a rhombus. The arrows mean “is a type of”, not a step in a calculation.RectangleRhombusSquare
A square is both a rectangle and a rhombus. The arrows mean “is a type of”, not a step in a calculation.

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Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The total number of shapes is 34 hexagons + 16 triangles = 50 shapes.
  2. A regular hexagon has 6 equal sides and 6 equal angles, so it satisfies the condition in step (2) of the algorithm: 6 sides (4 or more), all sides equal, all angles equal.
  3. Therefore, each of the 34 hexagons is classified as a regular polygon under the algorithm.
  4. An isosceles right-angled triangle has 3 sides, so it follows step (1): classify as a triangle.
  5. The triangle does not have all sides equal (it has two equal legs and one longer hypotenuse), so it does not satisfy the 'all sides equal and all angles equal' condition.
  6. Thus, each of the 16 triangles is classified as irregular under the algorithm.
  7. Only the 34 hexagons are classified as regular polygons.
  8. The fraction of shapes classified as regular polygons is 34 / 50.
  9. Simplify 34/50 by dividing both numerator and denominator by their greatest common divisor, which is 2.
  10. 34 ÷ 2 = 17, 50 ÷ 2 = 25, so the simplified fraction is 17/25.
  11. Check: 17/25 = 0.68, and 34/50 = 0.68, so the simplification is correct.
  12. Therefore, 17/25 of the total shapes are classified as regular polygons.

Reference answer: 17/25

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