How To Really Solve This Fun Geometry Puzzle? (II)

Difficulty level: Very easy!

Hemanth
Street Science

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How To Really Solve This Fun Geometry Puzzle? (II) — Whiteboard graphics showing a circle two radii that are perpendicular to each other. Along these radii lie the sides of a rectangle with length 4 units and breadth 3 units respectively. The area within this construction that is not occupied by the rectangle is shaded yellow. Shaded area = What??
Geometry Puzzle — Illustration created by the author (geometry not to scale)

I recently encountered this fun geometry puzzle from multiple sources. Although it is on the easy side, it managed to engage me and I had fun solving it. So, I thought I’d write about it.

We have a circle with the centre ‘O’. From this centre, we have two perpendicular line segments drawn along the radii that meet the circle at its periphery.

Inside this construction, we have a rectangle with a length of 4 units along the horizontal line segment and a breadth of 3 units along the vertical line segment.

Given this setting, your task is compute the area that is not occupied by the rectangle in the construction. This region is shaded in yellow. How fast can you solve this puzzle?

Spoiler Alert

If you wish to give this puzzle a try on your own, I suggest that you pause reading this essay at this point and go ahead with your attempt. After your attempt, you may continue reading.

Beyond this section, I will be explicitly discussing the solution to this puzzle.

Setting Up the Fun Geometry Puzzle

It is clear that the rectangle is going to play a key role in this puzzle. So, let us begin…

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