Mathematics & Geometry

How To Find The Area of The Semi-Circle? 🍉

A Fun Geometry Puzzle

This is another simple geometry puzzle I cam across on Twitter created by Catriona, who shares fun and aesthetic geometry problems.

This is one of those simple yet satisfying to solve puzzles 🌙

Here’s a hint: draw some lines …

I recommend you pause the article, grab your pen and paper, and give this a go. When you are ready, keep reading for the solution! ✒️

Solution

Given that the area of each small circle is 1, we can find its radius using the formula A = πr².

With that in mind, we will make use of the rectangle and construct a right-angled triangle as follows

Our goal now is to find an expression of R in terms of r.

Using the Pythagoras Theorem, we get

Now that we know r and R in terms of r, we can use the formula for the area of the semi-circle A = 1/2πr² to find our answer

And that’s our answer.

How amazing 👧

What was your thought process this time? Comment down below, I am eager to know :) 💞

Save and share the following list for the best math puzzles on Medium👇

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Love, Bella ❤️