Parallelogram 20 Level 1 18 Jan 2024Pi = 3.2?

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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. How big is a slice of Pi?

We all love pi, but it has a lot of digits!

Wouldn’t life be simpler if we just rounded it a little? Made it a bit more bite size?

Watch this video about the narrowly averted disaster, when pi almost officially became 3.2.

Luckily there was a mathematician passing by!

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

1 mark

1.1 Which state almost mistakenly legislated that pi was in fact equal to 3.2?

  • Alaska
  • Indiana
  • Washington
  • New York
  • (Not answered)
1 mark

1.2 Which classical problem was Edward Goodwin attempting to solve?

  • Squaring the Circle
  • Proof of the RiemannReimann Hypothesis
  • The Mutilated Chess Board Problem
  • The Seven Bridges of Konnigsberg
  • (Not answered)
2 marks

1.3 Which of these numbers, when rounded to 1 decimal place, would give 3.2?

  • 3.94
  • 3.14999
  • 3.141
  • 3.15
  • (Not answered)
2 marks

1.4 It may not be possible to construct a square with the same area as a circle, but can you find a square with the same area as this triangle?

What would its edge length be?

Correct Solution: 6 cm

2. Triangle tangle puzzle

3 marks

2.1 Six identical right-angled triangles fit inside a rectangle as shown in the diagram.

The rectangle measures 24cm by 29cm.

What is the total shaded area in cm2?

  • 180 cm2
  • 348 cm2
  • 30 cm2
  • 72 cm2
  • (Not answered)
Show Hint (–1 mark)
–1 mark

It looks like the rectangle has the same height as two of the triangles.

Can you find the height of the triangles by splitting up the shorter length of 24?

Show Hint (–1 mark)
–1 mark

It looks like the longer length of the rectangle is made of two long triangle sides (which we just found) and a bit left over.

Can we use this to find the shorter side of the triangle?

Show Hint (–1 mark)
–1 mark

Now knowing that the area of a triangle can be calculated by using 1/2 × base × height.

Find the total area for all 6 triangles.


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.