Geometry: several problems. Try

  • Thread starter Thread starter Nguyen Thanh Nam
  • Start date Start date
  • Tags Tags
    Geometry
Click For Summary
SUMMARY

The discussion focuses on solving geometric problems involving a triangle ABC and a pyramid SABC, where specific dimensions and angles are provided. The first problem involves calculating the square of the intersection surface between a plate alpha and the pyramid SABC, with the result being confirmed as 2a² / 3√3. The second problem, which remains unresolved, requires determining the height of a trapezium NMHE formed by the intersection of plate alpha and pyramid SABC, with the user questioning if MH represents this height.

PREREQUISITES
  • Understanding of basic geometry, specifically properties of triangles and pyramids.
  • Familiarity with geometric intersection concepts and surface area calculations.
  • Knowledge of perpendicularity in three-dimensional space.
  • Ability to interpret geometric diagrams and figures.
NEXT STEPS
  • Research the calculation of intersection areas in three-dimensional geometry.
  • Study the properties of trapeziums and their height calculations in geometric contexts.
  • Explore the use of geometric proofs in determining relationships between points in space.
  • Learn about the application of coordinate geometry to solve complex geometric problems.
USEFUL FOR

Students and professionals in mathematics, particularly those focusing on geometry, as well as educators seeking to understand complex geometric problem-solving techniques.

Nguyen Thanh Nam
Messages
14
Reaction score
0
Hello! see if you can get the results same as me ):
Triangle ABC with AB=AC=a, BAC=90 deg. SA is perpendicular to plate (ABC) @ A. SA=a, also! In SB: ES=2EB. H is in plate (SBC) so that AH is perpendicular to plate (SBC). Plate alpha consists of AE and perpendicular ro plate SBC. Figure out the Square of the intersection surface between alpha and Pyramid SABC.
I got it as 2 a^2 / 3 root3. I'm quite doubtful, about you?
The drawing: http://img.photobucket.com/albums/v...orum s/334.jpg
Thanks :-)
 
Last edited by a moderator:
Physics news on Phys.org
That was easy, but the thing I got suck is the second problem: Triangle ABC with B=90 deg, AB=BC=a. SA is perpen to plate (ABC) @ A; SA=a.root3. M is a random point in AB. E is the midpoint of SC. Let MB=x.
I 'm done with the first request: Prove that a plate alpha consists of ME and is perpen to plate (SAB) will always consist of a definited line (I got it out as EH with H is midpoint of SB)
The second one where I got stuck: Figure out the Square of the intersection surface made by alpha and pyramid SABC. I got the surface is NMHE (MN is parallel with BC, N belongs to AC) but I still can't calculate out the height of trapezium NMHE?
Figure: http://img.photobucket.com/albums/v381/maxpayne_lhp/Maths and Other Sciences for the forums/3.bmp
Thanks
 
Last edited:
Oh wait, for the second problem, is MH the height of NMHE?
 

Similar threads

Euclidean and non Euclidean geometries problems
  • · Replies 4 ·
Replies
4
Views
4K
Extremely hard vectors/geometry problem: Find the centre of a sphere
  • · Replies 2 ·
Replies
2
Views
3K