How do you find the surface area of a 3-D prism?
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T= L + 2B\n\nT is total surface area\nL is Perimeter x Height\nB is base area
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There are two ways to measure the area of a shaded figure. The third is by integral calculus.\n\nMethod 1. \n\nStep 1. Draw the figure on a graph paper by choosing suitable scales in x and y axes.\nStep 2. Count the small squares that are shaded. If a square is not whole, then count it as one if it is greater than half a square. Skip it if it is less than half. And of course, two halves make a whole.\nStep 3. Convert it to area by multiplying the number of squares with area of 1 square.\n\nMethod 2.\nCase 1:\nIf the figure is a polygon, draw diagonals from from corner points and break it down to triangles.\nNow, the area of triangles can be calculated mainly by two formulae.\n\nArea of a triangle = (1/2) base * altitude\n= square root of [s(s-a)(s-b)(s-c)] \n\nThe second formula is very useful and practised in surveying. Here, a,b, and c are the three sides of a triangle; and s is the semi-perimeter i.e. s=(1/2)(a+b+c)\n\nCase 2:\nIf the boundary of the figure is curved, the the matter is a bit harder. If it is a circle or a part of a circle, use formula: area= pi*r squared; pi is approximately 3.1416..  Or else, you have to replace the curve by a straight line such that the area remains the same by eye.\n\nBy integral calculus, area can be found by using table of formula.
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you can figure out the hypotenuse using the pythagorean theorem (a^2 + b^2 = c^2), so the hypotenuse is 10.\n\nAfter that, you just add up the areas of all the surfaces - For the triangles, its 6x8 divided by 2 = 24\n\nFor the rectangular faces, you do the following\n4x8 = 32\n4x6 = 24\n10x4 = 40\n\nAdd all these up and you get as surface area of 120.
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Surface Area=sqrt{3}a^2\n    Volume =(1/12)sqrt(2)a^3\nhttp://en.wikipedia.org/wiki/Tetrahedron
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to calculate the area of a 2-dimensional space you always multiply length x width, or in this case height\n\nC
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Base times height gives the volume of the prism.\nVolume of prramid= 1/3 x base x height =1/3 x 24=8 cubic inches.
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To cacultate the surface area, you first need to know what shape it is.  follow this link for many different equations and find the one for your shape.
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Let the breadth of each red rectangle be x\n\nSo, area of red portion = 4x + x(3-x)\n\nSo, area of white portion is (4-x)(3-x)\n\nSo, 4x+x(3-x) = (4-x)(3-x)\nor 4x + 3x -3x^2 = x^2 -7x+12\nor 4x^2-14x+12 = 0\nor 2x^2-7x+6 = 0\nor 2x^2-6x-x+6=0\nor(2x-1)(x-3)=0\n\nx=1/2 or 0.5 foot is the reasonable answer.
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Lateral Area\nThe lateral area is the surface area of a 3D figure, but excluding the area of any bases. Lateral Area is often abbreviated L.A. Imagine a soup can. Now cut down the side of the can and roll it flat. What was the circumference of the base is now the length of a rectangle. To find the area of this rectangle which is the same as the lateral area, multiply this length by the width, which was the height of the can.\nLateral Area of a prism: perimeter × height \nLateral Area of a cylinder: circumference × height. \nLateral Area of a regular pyramid: ½ perimeter × slant height. \nLateral Area of a right cone: ½ perimeter × slant height. \n\n\nThe lateral area of a regular pyramid or right cone is similar to that of prisms, but since each face is a triangle (or triangle-like), there is a factor of one half. The lateral area is thus half the slant height times the perimeter. The slant height is the distance from the vertex to the edge of the base where it is halfway between the base's vertices. If the pyramid is irregular and certainly if the cone is oblique, the surface area might not be calculatable using elementary techniques (which is a fancy way to say you may need calculus). It depends on if you can obtain the altitude (slant height) of each triangular face.\n\n\nSurface Area\nThe surface area of a figure is the sum of the area of all surfaces of a figure. Surface Area is often abbreviated S.A. The surface area of a prism or cylinder is the lateral area plus the area of each base. Since the bases for a prism or cylinder are congruent, this is often expressed as twice the area of the base.\nSurface Area = Lateral Area + n × Bases\nn = 2 for prisms/cylinders; n = 1 for pyramids/cones; n = 0 for spheres. \n\n\nThe surface area of a pyramid or cone is the lateral area plus the area of the single base.\n\nThe surface area of a sphere is equal to 4r2. Analogous to the unit circle is the unit sphere. Similarly, just as there are 2 radians of angle in one revolution, there are 4 steradians of solid angle in all directions.\n\nExample: Consider a right pyramid A-BCDE with vertex A and square base BCDE of length 20" on each side and a slant height of 26". What are its lateral and surface areas?\n\nAnswer: We don't need the height for this calculation, but we will calculate it anyway to stress the difference between slant height and height. The slant height is the hypotenuse of a right triangle where the height is one leg and 20"/2 = 10" is the other leg. Thus 102 + h2 = 262 or 100 + h2 = 676. Thus h2 = 576 or h = 24". The lateral surfaces are all triangles with a base of 20" and a height (the slant height) of 26". There are four of them. Thus the lateral area is 4×½×20"×26" = 1040 in2. The base is 20" square or 400 in2. Thus the [total] surface area is 1440 in2.\n\n  Understanding surface area may be clearer if you refer back to the net associated with the object. At left is a net for a cube and at right a portion of a net for a sphere. Each of these portions of a sphere is called a gore.\n\n Now is a good time to review something learned in algebra, namely (x + y)2 = x2 + xy + xy + y2 = x2 + 2xy + y2. The diagram at the right should clarify this further, help you remember the FOIL method, as well as give a physical basis for this relationship. (Remember also, the square root of (x2 + y2) does NOT equal x + y.) Consider extending the FOIL method first into trinomials: (a + b + c)(d + e + f) = ad + ae + af + bd + be + bf + cd + ce + cf. The distributive property is another way to consider this situation. Here the box method is useful.
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Diagram here:\n\nhttp://mathworld.wolfram.com/TriangularPrism.html\n\nto solve for its volume, calculate for the area of the triangle bottom and multiply it by the height of the prism.\n\nTo compute for surface area, compute for the area of the 3 rectangular faces and add the area of the 2 triangular faces.
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The simple way to find the area of any shape is to break it up in to trangles and squares.  \n\n\nOr use integration... but i do not think that is what you are looking for
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I can't imagine finding the surface area from just the volume without knowing the SHAPE OF THE OBJECT.
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Surface Area = 4*PI*r^2\n\nr = SQRT(SA/4/PI)
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Surface areas and lateral areas are always fun to find.  Surface areas for right prisms and cylinders is always the sum of the lateral area and two times a base.  (Lateral area is the sum of all the surfaces that aren't bases.)\n\nIn the case of a cylinder, the lateral area is really a rectangle - imagine cutting open a roll of toilet paper.  The length is really the circumference of the top (base) and the height is, well, the height of the roll.  So the lateral area is 2*pi*r*h.\n\nThe surface area is the lateral area plus two bases.  A base in this case is given by pi*r^2.  So the total surface area is 2*pi*r^2 + 2*pi*r*h.\n\nThe idea behind lateral and surface areas will carry over when you start working on right prisms (if you're not already doing those).  Lateral area is, in the case of a prism, the perimeter of the base (similar to cylinders, except we used "circumference" in place of "perimeter") times the height of the prism.  And the surface area is the lateral area plus two bases - in this case, the bases vary (you may have squares, triangles, trapezoids, etc.), so your formula for the total surface area will vary as well.\n\nThis is probably more than you wanted to know, but it's always good to relate things you know to things that you're learning.
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lateral surface area of a cone = pi*r*l\n\nwhere \n         pi = 3.14( a mathematical constant)\n         r = radius of base of cone\n         l = slant height of cone\n           =  square root of sum of squares of base radius  and height of cone\n         h = height of cone from centre of base circle to apex of cone\n          l = sq rt(r*r + h*h)
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Surface area:\nCylinder(lateral):2 times pie times radius times height\ncylinder(total): 2 times pie times radiuse times height + 2 times pie radius squared\nTriangular prism(total): find the area of every side and add all together to get surface area(hint:area of a triangle=1/2bh or bh/2)\nCone(lateral):pie times radius times length\nCone(total):pie times radius times length + pie squared\npyramid(total):find area of ever side and add all together \narea of a triangle=1/2bh bottom of the pyramid is length times width
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tricky question... you could probably get a fair approximation by looking at a computer model of the wonders and having the computer determine the surface area based on how much mesh is required to cover the model.\n\nIRL I would probably just take a model and see how much paint is required to cover the surface, that should give you a good estimate.