what is the most complicated three dimentional figure lais out as a two dementional figure?
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Two dimensional. It's a cross-section of a cone (a conic section - look up Euclid).\n\nAn ellipsoid is a three dimensional solid that has three perpendicular cross-sections that are ellipses. Many other 3D shapes have elliptical cross-sections - a prolate or oblate spheroid is pretty much spherical except one cross section is elliptical (the earth is an oblate spheroid, a rugby ball or american football is prolate).
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1.rectangle\n\n2.trapezoid
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Within your 3x3x3 cube, we have ten classes of rectangular prisms, including the two boundary cases of the whole cube and of the single cublet:\n1x1x1, 1x1x2, 1x2x2, 1x1x3, 1x2x3, 2x2x2, 2x2x3, 1x3x3, 2x3x3, 3x3x3.\n\nFor each prism class, we have to count all possible arrangements within the main cube. The contributes to this number are from translations, then from rotations (but only for non-symmetric prisms). If I'm not wrong, they are:\n1x1x1: 27\n1x1x2: 54\n1x2x2: 12\n1x1x3: 27\n1x2x3: 18\n2x2x2: 8\n1x3x3: 9\n2x2x3: 12\n2x3x3: 6\n3x3x3: 1\n\nTotal=174 prisms\n\nAs per your later addition, if we want to discard cubic prisms, we have: 174-27-8-1 = 138 non-cubic prisms.
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Trigonal planar.\n\n120 degrees.
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Here are some real tough ones.(Looked tough to me)\n\nProve that cot(90 - theta)sin(90 - theta) = sin theta\n\nFind Cos(3x)\n\nFind Sin(3x)
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there is no "forth" dimention, unless you mean back and forth, then it would just be forward :p\n\nanyway, the "fourth" dimention just refers to time.  There are 3 spacial dementions, and the 4th is time
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If it's 2-dimensional, it's a decagon.  If it's 3-dimensional, it's a decahedron.
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a trapezoid.\n   __\n  /__&#92;
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It actually becomes trivial at other dimensions.\n\nConsider 1 dimension, or basically a line. This space can be colored in 2 colors. One just alternates the two colors on the line.\n\nConsider 3 dimensions, or our normal space. Imagine a stack of cat food cans as high as you want. Next imagine that each can has a very long chop stick glued to it, and the stick and can are the same color. If the can is sitting flat on the ground, the stick will be straight up in the air - or perpendicular to the lids.\n\nStack the cans so that the sticks all ring around the cans, so that every can's stick touches every other can. Because each can/stick pair is one color, and each stick touches every other stick, in 3-space, you may need a unique color for each entity.\n\nBack to 2-dimensions for a moment.\n\nColoring a planar graph with 5 colors is fairly trival proof in graph theory.\n\n3 colors is never sufficient. Consider a graph where three nodes are all touching a central fourth node. You'll definitely need 4 colors for that.\n\nHowever, in order to determine whether any graph is colorable in 3 colors or not is not easy. In fact it's NP-Complete. Believe me I know. I struggled over that as a homework problem in complexity theory in graduate about 20 years ago. I think I still remember how to prove it.
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Each side would have length sqrt(3), so the area would be 3 m^2.
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Here are two (see refs.). Note that the second one is a rotating 3-D model.
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a trapezoid ia a quadrilateral with only two parallell sides.\n\nas to figuring out what CD is, i'd need to know what MA and HT are (are they lengths of sides? measurements of angles?)  so, if you post those, then i'll see what i can do
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number of sides, congurency?, size of angles, distinguishing characteristics
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just go straight across.\n\nlike:  3/8 x 2/3 = 6/24 which simplifies to 1/4\n\nBecause on the top: 3x2=6 and on the bottom: 8x3=24\nThen 6 goes into itself once and into 24 four times: 1/4
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a) isoceles\nb) hexagon\nc) hemisphere\nD) equilateral\ne) \nf)\nG) sphere or spherical\nh)\ni)\nj) scalene\n\nthese are the ones i know. next time, do your own homework!
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Surface area. Seriously. 8D