1001math: Area puzzles

Area puzzle

The 'Area puzzles' resource from the 1001math collection are a development of the ‘area maze puzzles’ first introduced in 2015 by one of the world’s most prolific inventors of logic puzzles, Noaki Inaba. He came up with the ‘area maze’ after being tasked with creating an easily accessible problem by the head of a crammer school in Japan.

Area puzzles are simple to explain: find the missing value which is denoted by a question mark. In the original puzzles the focus was on rectangles, but the examples from ‘1001math problems’ extend this to include triangles. The key that makes the puzzles such a challenge is that you are not allowed to use fractions (or decimals) in the solution. If you were allowed fractions, then the problems could be solved using standard algorithms. Adding the constraint demands greater use of mathematical reasoning skills.

Looking at the example, the left hand triangle reveals that the height must be 8 cm.

Knowing this information means that we can now calculate the height of the right hand triangle as being 8 – 2 = 6 cm.

The area of the triangle is 9 cm2, so with a height of 6 cm the base must be 3 cm.

The triangle shares a common side with the rectangle so the dimensions of the rectangle are 3 cm by 2 cm and the area is 6 cm2.

The ‘area and perimeter’ collection of resources from ‘1001math problems’ contains further examples of area maze problems, together with puzzles, activities, games and more.

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Age11-14, 14-16
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