Exploring the Area of the Shaded Region in an 8x5 Rectangle
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Chapter 1: Understanding the Puzzle
What do you perceive when you look at this figure? Personally, it resembles two spotlights, one blue and the other red, casting their beams toward the same point on a stage, creating an intense visual effect reminiscent of a theatrical performance or a concert.
The intriguing question arises: what constitutes the shaded areas of red and blue light? I encourage you to pause here, take out your pen and paper, and attempt to solve it yourself. Once you're ready, continue reading for the solution!
Solution
The crux of this puzzle lies in the diagonal of the rectangle, which divides the rays into four triangular sections.
Do you appreciate the contrast between purple and yellow? Let's examine the pair of purple triangles.
These two triangles feature a base measuring 1 and a height of 4.
Area = 1/2(1)(4) + 1/2(1)(4) = 4
Can you apply the same logic to evaluate the yellow triangles?
The yellow triangles also have a base of 1, but their height is 2.5.
Area = 1/2(1)(2.5) + 1/2(1)(2.5) = 2.5
Consequently, the total area of the shaded regions is:
Area = 4 + 2.5 = 6.5
Isn't that fascinating? I’m curious about your thought process while tackling this puzzle! Feel free to comment below; I’d love to hear your insights.
The first video titled "Find Area of the Shaded Region of a Rectangle" elaborates on how to calculate areas within geometric shapes, providing visual aids and step-by-step guidance.
The second video, "How to Find the Area of the Shaded Region | Rectangle in a Rectangle | Math with Mr. J," offers a practical approach to understanding shaded areas using real-life examples.
Chapter 2: Join the Community
Feel free to save and share this list of engaging math puzzles on Medium that covers various topics such as Algebra, Geometry, Calculus, and Number Theory.
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With gratitude,
Bella