Find the area of a triangle inside a square

[OysterOmelet]

@Poundsand

look at the solution @Andrew showed a little closer.

Looks like he did. Good job.

[Andrew]

@OysterOmelet

Good job, guys, but I stomped all of you. Doesn’t look like any of you made use of FA=FM.

Hmmm. You’re a day late, 0.000000000000004 cm off, with sloppy handwriting, and relied on software. I’m not sure about the “stomping”.

I’m giving you a C+.

[RickRoll]

So far, the simplest, more direct, and quicker solution had been proposed by @urodacus, maybe you guys missed it.

Make F=D, then AMD=1/2ABCD.

That’s it. Done.

[Andrew]

@RickRoll

So far, the simplest, more direct, and quicker solution had been proposed by @urodacus, maybe you guys missed it.

Make F=D, then AMD=1/2ABCD.

That’s it. Done.

Yeah, but that’s the wrong answer. F isn’t D, and AMD isn’t 1/2ABCD (which gives 32, rather than 30). I read their response as some kind of approximation if F was moved to the left.

That answer breaks the question, as in my second post above.

[Poundsand]

then d wouldn’t be the perpendicular bisector of AM.

[urodacus]

Ah. I missed the point of it being the bisector… read the f’n question properly, always a good first step. I just read that as being perpendicular.

[OysterOmelet]

@Andrew

Hmmm. You’re a day late, 0.000000000000004 cm off, with sloppy handwriting, and relied on software.

That’s just the way the program handles the rounding.

I only used the software for arithmetic as I’m on vacation and don’t have any pen or paper.

[VOT]

Wonderful! Your approach is a new one, different from others in the responses for this twitter post.

30cm^2 is a correct answer.

[VOT]

Wow! wonderful approach. I like it! It shares similar spirit of the math youtuber 3blu21brown.

[VOT]

This approach works for general condition in which area of the square is not given.

[VOT]

@fonserbc

Then since we know that E is at the middle point of AM (since d is a bisector), and we know that M is in the middle of CB: then we also know that H is in the middle of MB, and G is in the middle of DC.
This means that the length(EG) = 3/4 x

Finding the length(EG) is original!

[VOT]

You must also the one that likes 3blue1brown’s youtube videos.

[VOT]

Quite a few approaches taken by posters in Forumosa are actually original. I mean that they are not seen in the replies to this math question in the original twitter.

However, there are two approaches in the original replies that have not been thought of here. Here are the hints:
new approach 1.) Find the equation of the perpendicular bisector, and the coordinates of F.

linear algebra approach) Use the determinant to compute the area of the triangle.

[Explant]

@OysterOmelet

@Andrew

Hmmm. You’re a day late, 0.000000000000004 cm off, with sloppy handwriting, and relied on software.

That’s just the way the program handles the rounding.

I only used the software for arithmetic as I’m on vacation and don’t have any pen or paper.

you do this on vacation? I have a whole new level of respect for you.