Unlocking the Secrets of the Yellow Area: A Geometry Challenge
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Chapter 1: Understanding the Puzzle
Have you ever pondered how to calculate the total yellow area? The problem presents a red square with an area of 12 square units.
Source | All other images created by the Author
I stumbled upon this intriguing geometry puzzle on Twitter, shared by Catriona Agg. It’s a beautifully crafted challenge that offers numerous solutions.
Here's a tip: consider drawing some lines and think about triangles...
I encourage you to take a moment to pause, grab some paper, and attempt to solve it yourself. Once you’re ready, continue reading for the solution!
Section 1.1: Preparing for the Solution
Let’s begin by labeling the diagram for clarity.
The side length of the larger square is denoted as 'r', while the width of the yellow strip is represented as 'x'.
A key insight here is to visualize a right-angled triangle.
In this triangle, the hypotenuse is 'r', which also serves as the radius of the quarter circle. The adjacent side measures 'r - x', and the opposite side equals the square root of 12, reflecting the area of the red square.
Next, let’s determine the total area of the yellow section. We can achieve this by subtracting the area of the inner square from that of the entire square.
This is represented mathematically as:
Returning to the right-angled triangle, we can apply Pythagoras' Theorem to relate the three sides.
Can you see the path we’re following? By rearranging the equation, we can derive the precise expression for the area of the yellow strip!
And there it is—our solution! Isn’t it fascinating?
What were your thoughts during the process? Feel free to share in the comments; I’m eager to hear your insights!
Explore the video "Can You Find the Yellow Area of This Square? Test Your Math Skills Part 9" for further insights and challenges.
Section 1.2: Additional Resources
Check out the video "Find the Yellow Area" to deepen your understanding and tackle more geometry puzzles.
Chapter 2: Wrapping Up
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