Spoiler dala thynne hdapu wdhaYou have arrived at the answer.... but how it was worked out...
Uththare awata hadapu widiha waradida?You have arrived at the answer.... but how it was worked out...
------ Post added on Aug 5, 2024 at 5:15 PM
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Weekend Geometry Puzzle... 04_08_24
- Thread starter imhotep
- Start date
------ Post added on Aug 5, 2024 at 5:15 PM
මාත් cross view එක බලලා හදන්න ගියේ .. හැබැයි උබ ඔය කරල තියෙන්නේ cross එකම නෙවෙයි .. ආනත පැත්තකට ලම්බක view එකෙන් .. එහෙම හරි වගේ . නැත්නම් ඔය තිටා අර තිටා ම වෙන්නේ නෑ .
You have arrived at the answer.... but how it was worked out...
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Ammatahudu .. echchra dura hithuwe na hbai uththre awilla.
වික්ර්නෙට ලම්බක side view එකෙන් බලද්දී 90ට පෙන්වා නේද
Yes... The side with 3√2 cm and the 12 cm are at 90 degrees. So your answer holds.මගේ මොලේට මේකේ අවුල මොකක්ද තේරෙන්නේ නෑ
සමරූපි ත්රිකෝණ විදියට හැදුවෙ
එතකොට θ කෝනෙ සමානයිනෙ
4cmආව
@imhotep මාත් හරි නේද...
The main thing is the effort...which is appreciated. Thinking is brain food.
Alternate way which I mentioned as a hint somewhere in here.
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.
Solution: -
The small triangle area is obviously 1/2 * 6 * 6 = 18 sq cm
Each of the larger triangles 1/2* 6 * 12 = 36 sq cm
Thus the area of the shaded triangle = 144 - 2 * 36 - 18 = 54 sq cm
This gives us the area of the tetrahedron = 1/3 * base * height = 1/3 * 54 * h = 18h cu cm (consider the shaded area is the base as shown in the diagram)
Now, visualize the pyramid in another aspect. The upper vertex has three folds, each containing three 90 degree angled surfaces making contact.
If you take the smaller right angled surface of 18 sq cm as the base, you immediately realise that there is the 12 cm joining fold is perpendicular to this (as they all are 90 degrees)
This straight away gives us the volume of the pyramid from this perspective, 1/3 * 18 * 12 = 72 cu cm
Thus 18h = 72 or h = 4 cm.......
PS: Thanks for all those who tried or bumped the problem... Too many to mention individually. @icewiz came up with the first correct answer.
දැං තමා ඔයා කියන එක තේරුම් ගත්තෙThe main thing is the effort...which is appreciated. Thinking is brain food.
Alternate way which I mentioned as a hint somewhere in here.
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.
Solution: -
The small triangle area is obviously 1/2 * 6 * 6 = 18 sq cm
Each of the larger triangles 1/2* 6 * 12 = 36 sq cm
Thus the area of the shaded triangle = 144 - 2 * 36 - 18 = 54 sq cm
This gives us the area of the tetrahedron = 1/3 * base * height = 1/3 * 54 * h = 18h cu cm (consider the shaded area is the base as shown in the diagram)
Now, visualize the pyramid in another aspect. The upper vertex has three folds, each containing three 90 degree angled surfaces making contact.
If you take the smaller right angled surface of 18 sq cm as the base, you immediately realise that there is the 12 cm joining fold is perpendicular to this (as they all are 90 degrees)
This straight away gives us the volume of the pyramid from this perspective, 1/3 * 18 * 12 = 72 cu cm
Thus 18h = 72 or h = 4 cm.......
PS: Thanks for all those who tried or bumped the problem... Too many to mention individually. @icewiz came up with the first correct answer.
ඒ විදියට පරිමාව අරං මේ පැත්තටත් ඒ පරිමාවම දාල මේ පැත්තෙ උස හොයනව
ඒ පැත්තෙන් උස 12 යි මේ පැත්තෙන් උස 4 යි
උඹ කරල තියෙන දේ දැනුයි මට තේරුණේ
ඔයා කරල තියෙන්නෙ චතුස්තලේ හරි මැදින් දික් කඩ අරගෙන
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