Find area of the Blue shaded region | Two different squares | Important Geometry skills explained

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Find area of the Blue shaded region | Two different squares | Important Geometry skills explained

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[theoyanto]

Very clever way to solve this problem. And a very enlightening way to show the relationship of the geometry, I found this truly simple idea to be very very significant in my learning... it never occurred to me that clearly the sum of the squares was right there before my eyes.
Thanks for sharing this.
🤓👍🏻

[bunkerhill]

When I first looked at this problem the only thing I knew for sure was that there was insufficient information to answer it. When I saw the answer I laughed until well after tears came. Lesson learned!

[owlsschoolofmath]

I was surprised at how quick this came together!! My mind wanted to find the lengths of the sides but no need :)

[gerger]

2 problems in 1 day? You work very hard sir. This problem is very satisfying ❤

[misterenter-izrz]

The answer is a^2+b^2, where a, b are sides of two squares, so by pythagoras theorem, the answer is just 25^2=625.😃

[yalchingedikgedik]

Very nice and useful
Very simply solved
Thanks PreMath
Thanks Sir

[peterkrauliz]

Since no other dimensions are given, one can shift the whole 25 units length AB line to the left until it becomes vertical. As a side effect the small square becomes zero and the large square remains with side lengths 25. 625 easy as!!!

[kennethstevenson]

Amazing! Once the variables are added to the drawing the answer is obvious!

[jackwhite]

Very beautiful. Thanks. In similar cases it is useful to give the supplementary statement that the result is valid for many a and b values between 0 and 25

[lardyify]

If the small square were drawn outside of the triangle, the answer would have been obvious. As it was, I was completely fooled by this fantastic puzzle.

[alster]

Paused midway and solved it on my own. I knew it was 625 sq units after all. Fast forwarded till the end after solving and my answer did match with the one in the vid

[geoninja]

625.... solved in a few seconds looking at the opening frame.... :)

[procash]

Nice. Very simple solution😊😂

Initially I thought it would be complicated process 😅

[kennethwright]

Based on 3, 4, 5 ratio, looks like ll=20 and l=15, so small square area = 225 and large square area = 400, so total 🟰 625 units

[vidyadharjoshi]

Let AC = A, BC = B. Asq + Bsq = 25sq = 625 which is also the area of blue region.

[marcovargasglobant]

Too easy!!! naked eye with pitagoras: total area = 25²

[batavuskoga]

At first, I thought we have to calculate the values of the square's sides, I couldn't figure it out.
Then suddenly I saw it. In fact it's very simple, but you have to see it.

[dhrubajyotidaityari]

Invert the small square upward and draw another upon the 25 length. The fig now'looks like the pyth.. theorem proof.

[geoninja]

With these problems with next to no info, I find it helpful to assume an extreme case, where one variable is zero.... more an Olympiad solve I guess... :)

[AmirgabYT]

I didn't expect the ending of the solution would be so unusual 😂😂😂😂