Exploring the Area of a Semi-Circle: A Fun Geometry Challenge
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Chapter 1: The Geometry Puzzle
Let’s embark on a journey into the world of semi-circles! Today, while enjoying some refreshing watermelon and crispy fried chicken, I couldn’t help but think of a fun geometry puzzle shared by Catriona on Twitter. Have you had a satisfying meal today?
Before diving into the challenge, I suggest you pause here, grab some paper and a pen, and give this puzzle a try. Once you feel ready, continue reading to discover the solution!
Section 1.1: Understanding the Setup
In this puzzle, we’ll connect the top of the red line to the yellow line, meeting at the center of the circle.
Suppose the base of the left triangle measures x. Consequently, the base of the right triangle would then be represented as 6 - x. Both triangles share a hypotenuse, which we’ll denote as the circle's radius, r.
Now, it’s time to apply the well-known Pythagorean Theorem to this scenario.
Section 1.2: Solving for x
By equating the two triangles, we can solve for x.
After determining that x equals 2, do you see the next step? We can substitute this value back into one of our previous equations to find the radius, r.
Now that we have the radius, let’s recall the formula for the area of a semi-circle.
Chapter 2: Area Calculation
Now that we understand the components, let’s delve into the area calculation.
The first video titled "How To Calculate The Area of a Semicircle" provides a great overview of the process. It breaks down the formula and explains how to apply it effectively.
Additionally, the second video, "Area of a Semicircle from Diameter and Radius | Geometry," offers further insights into determining the area based on different parameters.
As we conclude this puzzle, remember the playful debate: pies or pi? Ultimately, we arrive at our solution.
How fascinating! What was your thought process while solving this? I’d love to hear your insights in the comments below!
Math Puzzles
Explore a curated list of intriguing math puzzles available on Medium that span various topics, including Algebra, Geometry, and Calculus. Share them with friends for a fun challenge!
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