Geometry: several problems. Try

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The discussion revolves around solving geometry problems involving triangles and pyramids. The first problem involves calculating the square of the intersection surface between a plane and pyramid SABC, with a proposed solution of 2a^2 / 3√3. The second problem, which is more complex, requires finding the square of the intersection surface formed by a plane and pyramid SABC, with the user struggling to determine the height of trapezium NMHE. Clarification is sought on whether MH represents the height of NMHE. The conversation highlights the challenges of geometric calculations and the need for precise definitions in problem-solving.
Nguyen Thanh Nam
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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 :-)
 
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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
 
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Oh wait, for the second problem, is MH the height of NMHE?
 

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