Dissecting octagon into parallelograms

Consider a regular octagon with side length 1, tiled with a finite number of parallelograms. Find the total area of all rectangles among these parallelograms.

(Squares are considered rectangles)

Edit: The point is to find all possible values of the total area.

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Abandoned square building became a parallelogram over time
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What is the visual intuition for the cross product of two vectors being the area of a parallelogram formed by the vectors joined at a common point?

We are told in various textbooks that the determinant of a matrix formed by three vectors, with the coefficients of the coordinate components making up the rows, can be interpreted as the volume of the parallelepiped formed by the vectors on the same coordinate system (or more technically the spatial distortion on those coordinates).

We are also told that the determinant of the cross product of two vectors is the area of the parallelogram formed by the two vectors joined end-to-end.

The cross product matrix of the two vectors can be interpreted as a matrix having three vectors (the vector <i,j,k>, in addition to the two vectors) joined end to end. The volume of the parallelepiped formed by these three vectors would indeed be equal to the area of the parallelogram, when these two vectors lie on the xy, xz or yz plane (as height would be equal to 1). However, if they do not lie on this plane, the height can vary between zero and root (3).

Hence the volume of the parallelepiped would not be equal to the area of the parallelogram unless the vectors lie on the axes plane. But we are told in calculus classes that we can use the the cross product to find the area of a parallelogram in any case.

Where am I wrong here?

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What do the lines on the parallelogram pointing to 8 o'clock on this portside clock face represent?
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Time lapse question - Anyone know why the video frame would be distorted as shown? It's kind of parallelogram shaped and the time stamp is mostly cut off. This is straight off the microSD card and they're all like this.
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I only subscribe to Mandela Effect and related subreddits because seeing people lose their shit over bad memories and blaming CERN or parallelograms is amusing to me.
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Oh to be a parallelogram
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Parallelogram shaped ship
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Rotating 2D Square distorts it to a parallelogram

So I googled this and this is the only useful result I got:

https://answers.unity.com/questions/222018/rotating-an-object-distorts-it.html

Sadly it does not help me though.

The square I have is a child of something and just rotating it on the Y-angle distorts it to said shape. The stated solution didnΒ΄t solve it either it still happened.

I feel like this is a common and basic mistake/error but I am unable to fix it. Can anybody help please?

Edit: I did the rotation via

transform.rotation *= Quaternion.AngleAxis(1, Vector3.up);

but it is unimportant since rotating it via the inspector causes the same distortion.

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Dissecting octagon into parallelograms II

Inspired by this riddle

Consider a regular octagon of side length n. How many ways are there to dissect the octagon into parallelograms with side length 1? You may assume that the vertices of the octagon are labeled (so that you do not need to deal with considering two dissections equivalent if they are the same after rotation).

For a slightly easier variant, use a regular hexagon. For a harder variant, what is the answer for an arbitrary 2m-gon?

Edit: Here is a picture made by /u/JWson of an example when n=1. In this case, every example will be a rotation or reflection of this example, and so there are 8 tilings. In the case of a hexagon, when n=1, there are 2 tilings, which are rotations of each other.

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A few days I posted about a blanket I was working on with hdc in the third loop. Unfortunately it came out parallelogram-shaped πŸ€·πŸΌβ€β™€οΈ so I frogged it and replaced it with this bobble stitch. At least this one has straight sides!
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I don't understand how you apply parallelograms of forces, can anyone help, please?
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Starting a scarf and it’s working out at an angle, almost like a parallelogram- is this normal or am I doing something wrong?
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Parallelogram mount recommendation

I have a pair of Celestron 15x70 binoculars that were absolutely amazing to look through last night. Standing at the tripod and contorting my neck all sorts of weird directions was not amazing. I'm 95% sure I want a parallelogram mount. More specifically, I want the kind with the L bracket that allows the tripod to be off to the side and lowered down to where the user is sitting comfortably in a chair. Some of the cheaper ones have the mount and tripod in front of the user.

I keep seeing the Orion 05752 Monster Mount & Tripod. That's currently $500 on Amazon. I might as well buy a dob for that price. What rise can you wonderful folks recommend?

One other question: until last night I was planning on spending some of my bonus next spring to get a 10 or 12 inch dob ($1k range), but after last night, I think I'd rather spend a few hundred to make the binoculars more enjoyable. The whole point is to use this stuff, right? I find it more likely that I'll get out binoculars and a chair than a huge scope. Moreover, we have a family membership with our local astronomical society, and once Covid is over, I plan on getting trained on their scopes that I can drive 20 minutes to use any time.

Bottom line: I would rather spend money on binocular equipment that I'll use at home more often and avail myself of astronomy club gear once Covid passes. Is that a good idea?

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This parallelogram-shaped (i think) book I found about the leaning tower of Pisa
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What would happen if they skipped teaching parallelograms (and other subsequent math portions) and instead taught taxes at school?
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Finished at last! Every parallelogram outlined by hand with embroidery floss.
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Help me! My blanket is coming out as a rhombus! Or parallelogram...a shape unlike a blanket.
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Help please! Vector/parallelogram problem

My teacher had some tech issues so maybe I missed something in his lecture videos videos?Still, I’ve spent two days messing with this thing and I still feel like I’m nowhere close. The deadline was at midnight so I’m just asking now because I feel that I really need to learn how to do this type of problem. It seems super straightforward since vectors B and D should be parallel, right?

Parallelogram ABCD

A=(-3,5); B=<1,b>; C=(3,6); D=<a,4>

Find values of a and b

(Note: Numbers between arrows are vectors, not Cartesian points)

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A square = parallelogram?

Is it true a square is a parallelogram?

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Find area of a parallelogram and volume of a parallelepiped bounded by vectors using CASIO fx-115ES (16) youtube.com/watch?v=5SD9B…
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Why isn’t the area a parallelogram the same as a rectangle?

So I was doing a math assignment and this is really twisting my head.

The area of a parallelogram is Length * Height

The area of a rectangle is side a * side b.

Isn’t a parallelogram just a tilted rectangle?????

Please send help so I can stop thinking about it.

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Parallelogram / Shapes Tutorial / using HTML and CSS youtube.com/watch?v=2Et-v…
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Parallelogram
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Parallelogram / Shapes Tutorial / using HTML and CSS youtube.com/watch?v=2Et-v…
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Parallelogram / Shapes Tutorial / using HTML and CSS youtube.com/watch?v=2Et-v…
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Cant do trigonometry in parallelogram, trapezoid and rectangle. Please anyone can help me?

I have a test after new years, and i really need to learn trigonometry but in triangle, trapezoid , rectangle and Parallelogram. Couldnt find any video helpful for these forms, every video is whether circle, or a normal rectangle. any help or a link would be helpful please.

its my college preparation exam, so i guess its all high school level if that makes any sense.

thanks in advance.

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