Parallelogram 29 Level 1 21 Mar 2024Making the cut

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Noun: Parallelogram Pronunciation: /ˌparəˈlɛləɡram/

  1. a portmanteau word combining parallel and telegram. A message sent each week by the Parallel Project to bright young mathematicians.
  • Tackle each Parallelogram in one go. Don’t get distracted.
  • Finish by midnight on Sunday if your whole class is doing parallelograms.
  • Your score & answer sheet will appear immediately after you hit SUBMIT.
  • Don’t worry if you score less than 50%, because it means you will learn something new when you check the solutions.

1. Dissections

Since ancient Greek times mathematicians have enjoyed dissection puzzles.

They’re less painful than they sound!

The aim is to transform one shape into another, like this rectangle which has been transformed into a square.

You may recognise this from the centuries-old popular game of Tangrams.

Relax and watch this oddly satisfying video where the process of dissection is used to create each of the named quadrilaterals.

(If you have problems watching the video, right click to open it in a new window)

1 mark

1.1 How would you describe the process of “dissection”?

  • Cutting and rearranging
  • Folding
  • Bending and stretching
  • Shifting into another dimension
  • (Not answered)
2 marks

1.2 What happens to the area of the shape when it is dissected?

  • Doubled
  • Halved
  • Stays the same
  • Quadrupled
  • (Not answered)
2 marks

1.3 Here you can see a square transformed into a triangle by dissection.

If the base of the square is 6 and the base of the triangle is 8, what is the height of the triangle?

  • 3
  • 4
  • 8
  • 9
  • (Not answered)
Show Hint (–1 mark)
–1 mark

Remember to find the area of a triangle we use the formula half × base × height.

The area of the triangle is the same as the area of the square: 6 × 6 = 36.

We are told the base of the triangle is 8.

So half × 8 × height = 36.

Which value would work in place of the height?

2. Some more geometric fun

2 marks

2.1 What fraction of this triangle is shaded?

  • 116
  • 112
  • 18
  • 16
  • (Not answered)
Show Hint (–1 mark)
–1 mark

Think about what fraction of this triangle is shaded, and compare it to the section we want.

Not all of the lines in the diagram are helpful!

Before you hit the SUBMIT button, here are some quick reminders:

  • You will receive your score immediately, and collect your reward points.
  • You might earn a new badge... if not, then maybe next week.
  • Make sure you go through the solution sheet – it is massively important.
  • A score of less than 50% is ok – it means you can learn lots from your mistakes.
  • The next Parallelogram is next week, at 3pm on Thursday.
  • Finally, if you missed any earlier Parallelograms, make sure you go back and complete them. You can still earn reward points and badges by completing missed Parallelograms.

Cheerio, Simon and Ayliean.