Parallelogram 43 • Level 2 • 26 Jun 2025The little hexagon that could
Noun: Parallelogram Pronunciation: /ˌparəˈlɛləɡram/
- 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. The largest small hexagon
What does it mean for a shape to be small? And how can one be the largest small shape?
Don’t worry, Dr. James Grime is here to show us this quirky little hexagon.
(If you have problems watching the video, right click to open it in a new window)1.1 What does it mean for a shape to be “small”?
- It can’t be seen by the human eye
- It has diagonal length 1
- It has fewer than 7 sides
- There exists a shape which is bigger than it
- (Not answered)
1.2 How much larger is the largest small hexagon’s area compared to the regular hexagon?
- Twice as big
- 4% larger
- 50% larger
7 6 - (Not answered)
1.3 Using the fact that the area of an equilateral triangle with side length 50cm is around 1082cm2.
Find the area of this hexagon with diagonal 1m (100cm).
- 180 cm2
- 6492 cm2
- 3246 cm2
- 541 cm2
- (Not answered)
Think about how many equilateral triangles would fit inside the hexagon.
2. Angle Tangle
2.1 The diagram shows a regular hexagon with an equilateral triangle inside it.
What is the size of the marked angle?
- 12°
- 15°
- 20°
- 30°
- 60°
- (Not answered)
Consider two useful facts:
All three angles in a triangle total 180°.
All six angles in a hexagon total 720°.
2.2 The diagonals of a hexagon split the shape into 13 pieces.
What fraction of the whole shape is the hexagonal piece in the center?
1 2 1 3 1 4 1 5 - (Not answered)
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.