Discovering the Shaded Area of a Square: A Geometry Challenge
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Chapter 1: Introduction to the Puzzle
What fraction of the square is shaded? The dots are evenly spaced.
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This geometric puzzle can be tackled using basic mathematical techniques. I'm curious to see how many individuals this challenge can engage, given that only about 0.25% to 2% of my followers typically view my articles unless the algorithm favors them. Perhaps I’ll share some statistics in a future post.
I encourage you to pause here, grab some paper and a pen, and give it a try. Once you feel ready, continue reading for the solution!
Section 1.1: Understanding the Solution
To grasp the solution, first observe the three straight red lines drawn on the figure. These lines divide the shape into two larger triangles and three smaller ones.
Interestingly, we can relate each triangle from the right column to the remaining sections of the figure. Given that the dots are evenly spaced, the area of the cross shape is equal to two out of three columns, leading us to conclude that the answer is 2/3.
Adding an X
Incorporating an X into the diagram results in a composition of smaller squares and triangles. It's essential to note that two triangles are equivalent to one square.
To find the solution, we count the total number of squares and triangles:
? = 3(4) = 12 and ? = 3(4) = 12.
Thus, the total area equals 12 + 12(1/2) = 18 squares. Consequently, the answer simplifies to 12/18 = 2/3.
What a fascinating challenge!
How did you approach this problem? I would love to hear your thoughts in the comments section below.
Chapter 2: Engaging with Math Puzzles
The first video, "MATHS PROBLEM STUMPING EVERYONE! Fraction Of Square Shaded," dives into the complexities of this intriguing puzzle, offering insights and strategies for solving it.
The second video, "What fraction of the square is shaded? | Tricky Math Problem," presents an engaging exploration of how to approach this challenge, enhancing your understanding of geometry.
Thank you for taking the time to read through this puzzle. If you found the content valuable, please give it a clap!
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Happy Solving, Bella