Geometry question

I have to make a pyramid out of paper as part of an assignment. I already have a template for a basic pyramid, but I have to alter the dimensions of mine (shown in the attached image: the black kite is my base, and the two red triangles are faces). My question: could someone tell me/give me a way to figure out the dimensions of the other two triangles?

 

a^2 + b^2 = c^2

xD

 

I would just try and find the length of everything you can with pythagreon theorem and then find all of the angles you can. Once those are all filled in use the law of cosines or get clever with the orientation of the problem. Also, remember you know the lnegths of two of the sides for each face, so all you need to do is calaculate the third for each one.

 

As given, the question is incomplete since the apex of the pyramid could be any number of places above the centre line.

Very important in geometry is that you should never trust a diagram to be drawn exactly. But in this case, you may need to in order to answer the question. Mention this to your teacher, as it's bad.

What you need to trust is that the red lines at the top do indeed form an X, with four 90 degree angles around the point.

From there, you can work out the lengths of the top side of the red triangles shown, and then use that length to determine the position of the pyramid's apex.

Once you know that, it is relatively simple to calculate lengths to the bottom corner.

 

Is the angle opposite to the length 30 cm 0.5pi radians? Because if it is that shape cannot possibly exist. Would you mind posting the net with all the angles you know already labeled?

 

Unless I am miss understanding your comment Higgs, I am pretty sure they are 90 degrees and I don't see any reason why they couldn't exist. What appears to not be drawn to scale on the diagram is the top corner for the 2 red faces, they should be much further to the top left and top right on the diagram respectively.

 

I don't think that makes it impossible; it just makes it a tall pyramid.

Those top two red lines would be ~29.58cm long.

These would join together in the folding of the net, making that top corner like the corner of a cube.

 

5^2+5^2 = 50
and
sqrt(50) != 30

edit: It's an isosceles triangle with two sides of 5 cm and hypotenuse of 30 cm. That's what I understand from the diagram. If my understanding is accurate such shape cannot exist. The hypotenuse would have to be 7.1 cm.

 

Yeah that's true, but the other side doesn't have to be 5 cm in length even if the angle is 90 degrees. I havn't run the numbers but Jasmine's answer makes sense.

 

Higgs -- Are you're assuming those vertical red lines are parallel to the centre line? They're not.

 

Ah ok. That's why I asked. That's one lousy diagram then buddy. I would still like to see the diagram fully annotated so I can avoid misunderstanding like this and actually focus on the problem.

 

I'll second the very bad diagram comment. With problems like this the only things I assume are what's been told to me.

 

So is this accurate?


(Didn't bother with the last two angles, you can figure them out easily from the information that's already on there)

edit: Ok I actually read the question properly... Weeee I love wasting my time!

 

If our assumption that the red X is suggesting four right angles is correct, then the three figures we need are: the 29.58cm, the 3.54cm, and the 7.17cm lengths.

Use the first two to work out the position of the apex.

Then use that and the third figure to work out the length X of the remaining edge.

Two new triangles will then have lengths {8, 30, X}

You should find that X ~ 31.46

 

I am pretty sure we can prove those assumptions if we tried. Anyways, I think I used a slightly different proccess than you and came up with the same answer.

 

^ no we can't prove them, because there is a free variable without the assumption.

That kite shaped base can be squashed/stretched thinner/fatter unless one of it's angles is fixed one way or another.

 

If the diagram was any accurate then yes we could but I think we have clearly demonstrated that it is a very poor approximation visual-wise. Based purely on the numbers already provided we cannot prove that.

 

Giving it a third solid look, I agree. Which makes me wonder if there something missing from the question. I have a hard time believing a question like this was written without the potential to find an answer.

 

Well, I'm an idiot.

Posting an edited pic in the hopes that it'll be more clear. Also, the image is not to scale, and I can't figure out the angle measurements for the "new" pair of triangles.

 

You've still got a free variable try again.