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Puzzles

One activity that many of our members enjoy is puzzling! You can test yourself for fun with our brainteasers. Our quizzes and conundrums are updated regularly, so do check back on the page for the latest content, and if you get really good at them, why not find out what your IQ is by booking a Mensa Supervised IQ Test?

16/3/25 – Arrowhead

What fraction of the square ABCD is covered by the arrowhead?

Length AX = 2 x Length XB

Length AZ = 2 x Length ZD

Y is the midpoint of DC

O is directly above Y and level with Z

Puzzle courtesy of Mensa member Peter Hooton

  • Show Answer

One Third

To avoid unnecessary algebra, assume the square is of length 6.

Therefore, AB = BC = CD = AD = 6

AX = AZ = 4,  DY = YC = 3   and   DZ = OY = 2

Area of the square ABCD = 36

Area Arrowhead = Area Square – Area of 3 Triangles

Area Triangle = base x height / 2

Triangle  AXD = 6×4/2 = 12

Triangle BXD = 6×2/2 = 6

Triangle OCD = 6×2/2 = 6

Area Arrowhead = 36 – (12 + 6 + 6) = 12

Puzzles for business use

We are also able to supply puzzle content to businesses, tailored to your needs. This can range from one-off media projects for marketing campaigns and content for newspapers, magazines and company websites, to long-running partnerships and licensing agreements.

Find out more by contacting our marketing team, via: communications@mensa.org.uk