Geometry: several problems. Try

  • Thread starter Nguyen Thanh Nam
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In summary, the conversation is about solving math problems involving triangles and planes. The first problem involves finding the square of the intersection surface between a square and a pyramid, and the second problem involves finding the height of a trapezium formed by the intersection of two planes. The conversation includes diagrams and calculations, and one of the participants is asking for confirmation on their solution.
  • #1
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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  • #2
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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  • #3
Oh wait, for the second problem, is MH the height of NMHE?
 

1. What is the difference between a line and a line segment?

A line is a straight path that extends infinitely in both directions. A line segment is a portion of a line with two endpoints.

2. How do you find the area of a triangle?

To find the area of a triangle, you can use the formula A = 1/2 * base * height. The base is the length of one side of the triangle and the height is the perpendicular distance from the base to the opposite vertex.

3. Can a triangle have two right angles?

No, a triangle cannot have two right angles. By definition, a right angle is exactly 90 degrees, and the sum of the interior angles of a triangle is always 180 degrees. Therefore, if one angle is 90 degrees, the other two angles must add up to 90 degrees, which is not possible.

4. What is the difference between a rectangle and a square?

A rectangle is a quadrilateral with four right angles and opposite sides that are equal in length. A square is a special type of rectangle with four equal sides and four right angles.

5. How many sides does a hexagon have?

A hexagon has six sides. The prefix "hexa" means six, and "gon" means angle or corner. Therefore, a hexagon has six angles or corners.

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