Weekend Geometry Puzzle... 04_08_24

[imhotep]

A 12cm x 12 cm piece of cardboard is maked as shown below. The dotted lines are drawn from the bottom left corner to the mid-points of the two opposite sides.
Now, the cardboard is folded along the dotted lines and position the white triangles upwards so they touch, you get a pyramid with height h.

Find: The height of the pyramid "h"




Pyramid formed with the traingles folded...




PS: You do not need solid geometry.... Think differently.

 

[Stimulus mind]

බම්ප් තමයි, සහෝ.

 

[Schrodinger Cat]

bump

 

[MrFrog]

bump

 

[Tricle_Buwa]

4.25 cm?

 

[imhotep]

4.25 cm?

Close but not the answer... Thanks for trying.

 

[jamiezue]

9/wargamoola 3
5.196?

 

[MrFrog]

3.79... something ?

 

[jamiezue]

OK my first try was through chat GTP. because I was on a bus at that time. But I think I got it now. So the hight of a pyramid is the closest distance to the base to the apex. right.? SO there are 3 white angles . All you have to do is find the closest distance from each vertices which are on the big square of white triangles to the closest base of the brown triangle. We have 3 of them. So you have to choose the shortest length of all of them . Am I right @imhotep . Indeed @Tricle_Buwa 's answer is really close

Edit- wrong

 

[icewiz]

4 x (7)½= 10.4 cm ?

වැරදි ඇති 10ක් එන්න බෑ වගේ

4cm?

Spoiler

 

[AnuradhaRa]

Orthocentre එකේ තමා මැද පොයින්ට්, එක මුදුණ තියෙන්නෙ

 

[hemantha06]

√(63/2)cm
5.61cm
Waraduna

 

[icewiz]

@dilann

 

[dilann]

3.7349698794 ?

---

oh පොඩ්ඩක් wait ....
------ Post added on Aug 5, 2024 at 5:00 PM

 

[hemantha06]

h=4cm

 

[AnuradhaRa]

බලියක් ඇන්ද, හදාගන්න බැරුව ගියා තාම ඔලුවෙ පොට යන්නත් වගේ එනව

 

[imhotep]

h=4cm

How did you get it?

Tip: It's a Tetrahedron.... We know the volume is 1/3 x base x height. The area of the shaded base can be easily calculated, because the areas of the three traingular sides are easy. Now think a bit of another way to get at the volume of the pyramid. Then you have the answer.

 

[AnuradhaRa]

How did you get it?

Tip: It's a Tetrahedron.... We know the volume is 1/3 x base x height. The area of the shaded base can be easily calculated, because the areas of the three traingular sides are easy. Now think a bit of another way to get at the volume of the pyramid. Then you have the answer.

හයියෝ අපි පරිමාවක් ගැන හිතුවෙ නෑනෙ... වර්ගඵලෙන් තමා ගොඩදාගන්න කල්පනා කෙරුවෙ

 

[dilann]

මේකද ??

4.0249223595

 

[imhotep]

4 x (7)½= 10.4 cm ?

වැරදි ඇති 10ක් එන්න බෑ වගේ

4cm?

Spoiler

View attachment 234191

You have arrived at the answer.... but how it was worked out...