Finding length in regular pyramid

In summary, the regular pyramid T.ABCD with a square base of side 1 cm has a mid-point of AB at N. The length of TN cannot be determined without knowing the height or slant-edge length of the pyramid. The only way to find the length of TN would be to leave it in terms of an unknown constant, such as AT, or to assume that the "regular" in the pyramid's name implies a specific relationship between the apex and the base. It is also possible that the answer is 1/2 √3, but this cannot be confirmed without further information about the pyramid's dimensions.
  • #1
songoku
2,266
319

Homework Statement


Regular pyramid T.ABCD has square base with side 1 cm. N is the mid-point of AB. Find the length of TN


Homework Equations


not sure


The Attempt at a Solution


No information given about the height of the pyramid and the length of the slant-edge, such as TA, so how can we find TN :confused:
 
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  • #2
Without being given the height of the pyramid (or something equivalent, such as the slant height) then you can't place a value on the length of TN. The only way I can see going about this is to leave the answer in terms of an unknown constant, such as AT, or maybe regular pyramid means something more than just the apex of the pyramid is normal to the centre of the base.
 
  • #3
Mentallic said:
Without being given the height of the pyramid (or something equivalent, such as the slant height) then you can't place a value on the length of TN. The only way I can see going about this is to leave the answer in terms of an unknown constant, such as AT, or maybe regular pyramid means something more than just the apex of the pyramid is normal to the centre of the base.

Not sure, but I think regular pyramid means that the apex of the pyramid is normal to the centre of the base and the base has equal side, i.e the base is square.

If I remember correctly, the answer is 1/2 √3. But I can't find it. I have provided the complete question
 
  • #4
songoku said:
Not sure, but I think regular pyramid means that the apex of the pyramid is normal to the centre of the base and the base has equal side, i.e the base is square.

If I remember correctly, the answer is 1/2 √3. But I can't find it. I have provided the complete question

Ahh ok then, with the answer of [tex]\frac{\sqrt{3}}{2}[/tex] that means the edges connecting to the apex are a length of 1 each, which I guess is what was also implied by the "regular" pyramid.
 
  • #5
Mentallic said:
Ahh ok then, with the answer of [tex]\frac{\sqrt{3}}{2}[/tex] that means the edges connecting to the apex are a length of 1 each, which I guess is what was also implied by the "regular" pyramid.

Ahhh you are correct. Thanks :smile:
 

1. How do you find the length of the base of a regular pyramid?

To find the length of the base of a regular pyramid, you can use the formula: l = s√(4h2+s2) where l is the length of the base, s is the length of one side of the base, and h is the height of the pyramid.

2. What is the formula for finding the slant height of a regular pyramid?

The formula for finding the slant height of a regular pyramid is: ls = √(h2+(s/2)2) where ls is the slant height, h is the height of the pyramid, and s is the length of one side of the base.

3. Can you use the Pythagorean theorem to find the length of a regular pyramid?

Yes, the Pythagorean theorem can be used to find the length of a regular pyramid. It can be applied to the triangle formed by the height, half of the base, and the slant height of the pyramid.

4. How do you find the surface area of a regular pyramid?

To find the surface area of a regular pyramid, you can use the formula: A = (1/2)bpls + bpl where A is the surface area, bp is the perimeter of the base, ls is the slant height, and l is the length of one side of the base.

5. What is the volume formula for a regular pyramid?

The volume formula for a regular pyramid is: V = (1/3)Ah where V is the volume, A is the area of the base, and h is the height of the pyramid.

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