# Geometry: several problems. Try!

1. Jan 12, 2005

### Nguyen Thanh Nam

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: Jan 12, 2005
2. Jan 12, 2005

### Nguyen Thanh Nam

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: Jan 12, 2005
3. Jan 12, 2005

### Nguyen Thanh Nam

Oh wait, for the second problem, is MH the height of NMHE?

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