Year 10+ Puzzles

Solution: Which is Bigger?

Solution: Which is Bigger?

The Puzzle:

In the picture, is the area coloured green or the area coloured blue bigger?

Solution: Which is Bigger?

The Solution:

Let's draw grid-lines over the puzzle so that it's easier to calculate the areas:

Solution: Which is Bigger?

The area of the square is \(10 \times 10 = 100 \text{ square units}\).

The green areas are equivalent to the area of two circles of radius \(3\). So,

\(A(\text{green}) = 2 \times \pi \times 3^2 \approx 56.55 \text{ square units}\),
\(A(\text{blue}) = 100 - 56.55 = 43.45 \text{ square units}\).
So the green area is bigger.

Note: If I'd made the green circles just a big smaller, the blue area would have been bigger. For example, if I made the radius \(2.8\), the green area would have been approximately \(47.16 \text{ square units}\), and the blue area would have been \(52.84 \text{ square units}), which is larger.


This series of puzzles are for Year 10 or higher students, these puzzles tests your skills and also train you with problem solving and thinking out of the box


Year 10 students or higher

Learning Objectives

Solving puzzles

Author: Subject Coach
Added on: 28th Sep 2018

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