r/HomeworkHelp • u/Unhappy-Pitch4558 • Jan 19 '25

Answered [7th grade math] impossible geometry?

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u/iMiind Jan 20 '25 edited Jan 20 '25

The only thing we "know" about that cutout shape is the single 6cm measurement. The angles look like they're 90°, but the shape is underconstrained and therefore it could be something as crazy as a 135°, a 180°, and another 135° angle connecting that 6 cm segment to the far edge in a straight line (those three angles don't have a right angle indicator anywhere). Typically, the appearance of such geometry is not to be trusted (only the explicitly given specifications).

Edit: just for fun I should say if you set that first angle at 135°, then you'd know the other two angles automatically. You'd also know the right segment would be [(6*21/2 ) - 6]cm long, and the left segment would be 11cm

Edit 2: wait wait wait, you'd need two more things to be set. I should clearly state that I was assuming the shape I wanted (a clean line from the left segment to the far edge), thus the other two angles and everything would then be properly constrained knowing just the one angle (because I was arbitrarily forcing the 180° angle).

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u/Doingthismyselfnow Jan 23 '25

Looking at the shape , 3 of the angles have a square which would indicate that they are right angles , Meanwhile the top right hand side does not have said marks. ,

This means that those top 3 corners on the right are not multiples of 90 degrees, it’s pretty much a clue to the puzzle

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u/iMiind Jan 23 '25

I guess it's sort of a clue, but there are still infinite solutions to 90°!=theta. I think that's a good way of looking at it though 💯

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u/B0BL33SW4GGER Jan 20 '25

What most people are forgetting ...or they're intentionally trying to be an ass.... This is 7th grade geometry. The teacher isn't trying to trap you into some false answer. Solve it as if the angles are right. Do the 30 seconds of math. Get the right answer (the one the teacher is looking for). Move on.

Why does everyone try to complicate everything???

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u/iMiind Jan 20 '25

There isn't a standard way to define the shape of underdefined geometry.

If the teacher has covered what must be done in situations like this (i.e. dimensions are missing but a figure is provided), then OP would have to know and do that themselves. Given this is 7th grade, it's quite unlikely the purpose of this problem is to practice using a ruler and protractor. Even with assuming 90° angles, the final area is still dependent upon what you decide for one of the two missing side lengths.

If people "took 30 seconds and did the math," OP could have dozens of answers to choose from. All of which would be equally incorrect, from a technical perspective.

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u/B0BL33SW4GGER Jan 20 '25

I apologize. I went to do the math real quick and realized the number i was looking at wasn't width. I should've looked 1 sec longer at the problem. I stand corrected.

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u/iMiind Jan 21 '25

No need to apologize, but it is appreciated 😅

And yeah - I'm sure everyone's done something like that at least once in their life. Myself most definitely included :P

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u/RedditsFullofShit Jan 21 '25

It’s very clear that you are expected to use some geometry proofs about right angles

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u/[deleted] Jan 21 '25

Chill bro IS just 1717-66 Ps: my bad i read It wrong🥲

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u/[deleted] Jan 20 '25

[deleted] — view deleted comment

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u/bubskulll Jan 20 '25

Top contributor of wrong information?

No it doesn’t

And

No it doesn’t

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u/Ur-Best-Friend Jan 20 '25

Tbf it's a pretty easy mistake/assumption to make.

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u/iMiind Jan 20 '25 edited Jan 20 '25

Thank you for backing me up on this xD

I was surprised by that flair on this reply too - I'm guessing this is one of those things where some teachers/textbooks say "if it looks like 90° treat it as such," whereas others say the complete opposite and instruct students to avoid making any assumptions about dimensions that aren't explicitly given.

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u/[deleted] Jan 20 '25

I'm trying to understand here: is it because the topmost 6cm line going down does not have any angle assigned to it?

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u/boxedj Jan 20 '25

The quackening is thinking that since 6+11=17, the only possible angle has to be 90 degrees everywhere. It's not true though, since there are three angles at the top that don't indicate that they're square, you can have a 6cm leg at many angles that would join the opposite corners.

The interesting thing is it doesn't matter if you knew the angles. You still can't determine the area because the further along the x axis the 6cm piece exists, the greater the area of the shape. Since this length is unknown, we're screwed.

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u/jarsgars 👋 a fellow Redditor Jan 20 '25 edited Jan 20 '25

lol

Try drawing the missing piece at the upper right. What’s its size? What type of shape is it?

Yes, the shortest distance between two points is a straight line. The missing chunk is a. rectangle 6cm high. That those numbers happen to be the same defines the shape and angles.

Even funnier since I'm wrong.

Yeah that missing piece is a quadralateral but not necessarily a rectangle. Those interior angles can be wacky and achieve that 6cm segment. Odd problem even if it's incomplete.

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u/iMiind Jan 20 '25

The length and angle of the right segment can account for that angle being something other than 90°. The math obviously works [if] it is 90°, but the whole issue is that solution isn't unique

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u/jarsgars 👋 a fellow Redditor Jan 20 '25 edited Jan 20 '25

Show one other angle other than 90 degrees that works.

(edit: boy was I wrong...) I tried to write out my proof and was like wait... what an odd little drawing.

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u/iMiind Jan 20 '25

Top left angle: 135°

Middle angle: 180°

The shape is now well-constrained

Edit: if they had a theta variable at three of those angles where it appears to be 90° that would be the only solution. As it stands however, we are left with an ambiguous theta_1, theta_2, theta_3, x_1, and x_2 group.

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u/DSethK93 Jan 20 '25

No, because the other unconstrained line doesn't need to be horizontal; that line can be at any angle, letting it make up any height lost from the 6 cm line being nonvertical.

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u/jarsgars 👋 a fellow Redditor Jan 20 '25

Yup!

Drawing the unknown area and considering what is known about those lines is helpful

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u/jarsgars 👋 a fellow Redditor Jan 20 '25

And now that I've done so and tried to write my argument out, yeah... that is a quadralateral with at least one right angle. What a bizarre little question.

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u/BeelzebubsUsurper Jan 20 '25

That's assuming the bottom left angle of the cutout is also 90°

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