Discovering the Area of a Semi-Circle with a Given Square Size
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Chapter 1: Understanding the Problem
While I was at the coffee shop today, I couldn’t help but overhear a lively conversation about various businesses. This chatter disrupted my focus a bit. Now, regarding the puzzle at hand, a helpful suggestion would be to visualize an imaginary triangle positioned at the center.
Take a moment to pause this article, grab your pen and paper, and give this problem a try. Once you feel prepared, continue reading to find the solution!
Solution
Given that the area of the square is 40, it should be fairly simple to determine that the length of each side is √40.
In this scenario, let us denote r as the radius of the semi-circle, which creates a right triangle with r as the hypotenuse. The adjacent side corresponds to half the length of the square's side, while the opposite side is equal to the side of the square itself. With this information, we can apply the Pythagorean theorem.
Recall that the formula for the area of a semi-circle with radius r is (1/2)πr². This allows us to substitute r² into our calculations.
And that's how we arrive at our answer.
Bonus Challenge
What if the dimensions of the square were represented as n?
How intriguing! What was your approach to solving this? I would love to hear your thoughts in the comments below!
The first video titled "How To Calculate The Area of a Semicircle" offers a comprehensive guide on the topic, walking you through the steps necessary for finding the area effectively.
The second video, "Area of a Semi Circle," presents a visual approach to understanding the calculation, making the concept clearer.
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