how do i find the total area of a prism?
409615
actually it's lateral area plus 2 times the base\n\nif lateral area= L and base= B, then total area is L+2B
552905
The AREA of an isosceles triangle is found by taking 1/2 the sum of the long and short parallel sides, times the height. One way to compare this with the parallelogram is to take two copies, turn one 180 degrees and glue them along the equal (nonparallel) edges. \nYou now have a larger parallelogram - with one side composed of the sum of the original short and long parallel edges. Use the usual formula for the area of this parallelogram, then divide by 2 (since it is composed of two equal copies).
981062
The surface area of a sphere of radius 'r' is given by:\n\nsurface area = \n 4*pi*r^2\n \n\nNOTE: The value of p can never be known exactly, so surface areas of spheres cannot be calculated exactly. Common approximations for p are: 3.14, and 22/7. \n\nExample 1  if 'r' = 5 for a given sphere, and p = 3.14, then the surface area of the sphere is:\n\nsurface area = 4*pi*r^2\n\n         = 4 × 3.14 × 25\n\n         = 314
23271
The area of a triangle can be found by multiplying the base times the one-half the height.\n\nIf a triangle has a base of length 6 inches and a height of 4 inches, its area is 6*2=12 square inches
829290
2 X pi X  r = cirumference\n\npi X r squared = area
679609
Surface Area=sqrt{3}a^2\n    Volume =(1/12)sqrt(2)a^3\nhttp://en.wikipedia.org/wiki/Tetrahedron
551690
T= L + 2B\n\nT is total surface area\nL is Perimeter x Height\nB is base area
547584
the surface area is (1/2 X perimeter of base X slant height)\nthe total surface area is ((1/2 X perimeter of base X slant height) + (area of base))
548292
Assuming that an area may be dissected into triangles, then the area of each triangle is given by \n\nArea = (s(s-a)(s-b)(s-c))^(1/2)\n\nwhere s = (1/2)(a + b + c)\n\nand a, b, and c are the lengths of sides of each triangle -\n\nThe sought for area is (finally) the sum of all the areas of the triangles.\n\nGiven sufficient patience, any arbitrary area will be found.\n\n(Drawing a diagram while slogging through the exercise and looping around the separate triangles in the same direction can yield a shortcut whereby all of the internal perimeters eliminate each other, leaving only the perimeter of the original figure.)
276388
If an object is a parallelogram, we define its area to be its length multiplied by its height. Rectangles and squares are common parallelograms.\nIf you cut a parallelogram in half along its diagonal, you get a triangle with the same width and height, but half the area. Thus the formula for the area of a triangle is (1/2)*base*height where the name "base" has replaced the now meaningless label of "length".\nUsing these two formulas, you should be able to find the area of any polygon (a closed shape with straight sides) by cutting it up into these shapes of known area. For example, a trapezoid can be cut up into a rectangle and two triangles.\nThe perimeter of a polygon is the easiest measure. Just add up the lengths of all the sides.
522898
Imagine you unraveled the cylinder, the middle would turn into a rectangle, right? so to find the surface area, take the height of the cylinder and multiply it by the circumference of the circles at the bases, then add in the area of the circles. Circumference is 2(pi)r and area is (pi)r^2.
544364
You can divide the cube into 9 1x3x3 slices.\n\nEach one contains the following prisms:\n1x1x2: 12\n1x1x3: 6\n1x2x2: 4\n1x2x3: 4\n1x3x3: 1\nSubtotal 27 x 9 = 81\n\nYou can divide the cube into 6 2x3x3 slices.\nEach one contains the following prisms that weren't counted above:\n\n2x2x2: 4\n2x2x3: 4\n2x3x3: 1\n\nSubtotal 9 x 6 = 54\n\nThat's 135.\n\nIf you count the 3x3x3, you have 136.
175713
Your question is too complicated to appreciate the math in it, which is supposed to be the real beauty in the first place. Anyway, I have tried figuring it out and come with equations. I do not even want to try and begin substitution and end up with more complications. I just thought once you saw the relation, you would throw those 10 points my way.\n\nAssuming a to be sides of the squares of the prism and b to be the length of the rectangles, we know that the sum of all dimensions is 14a+5b. Now I do not even want to get started why you brought it the story of the equilateral triangle. You can just say the sum  of the dimensions is 61. Anyway, since any side of the trianle, as it is equiangular hence equilateral, is twice 14a+5b and 122, the sum of the dimensions will be 61. So your first equation is 14a+5b=61\n\nYou know the volume of the prism is the length X width X heiht = a x a x b = (a^2)b This is equal to the surface area. The surface area is the sum of all the areas on the prism and that is a^2+4ab. (How about you calculate how that came up?)\n\nSo there is your second equation, (a^2)b = a^2+4ab So then from 14a+5b=61, express a in terms of b or the other way around and plug it into the second equation and experience brutal complications and figure out what the variables are. I think you know it is too easy to calculate each dimension and area after that.
921006
Area = πab where a and b are the semi-major and semi-minor axis length
553954
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.
850259
here:http://www.cut-the-knot.org/Curriculum/Geometry/AreaOfParallelogram.shtml
46232
The volume of the pyramid is 1/3 the volume of the prism.\n\nTo prove this, look at a horizontal cross section of pyramid. Let A = the area of the base.\n\n\nIf the the height of the pyramid is h, look at a cross section of the pyramid at a height t above the base. Any one dimentional measurement x in the base, will have size x(h-t)/n in the cross section. Any two dimensional measurement, (area) will be multiplied by ((h-t)/h)^2, i.e. A((h-t)/h)^2.\n\nNote\nNow integrate for t = 0 to h, A((h-t)/h)^2 dt\n\nYou get -A/3(h - t )^3/h^2.\nEvaluating at t = 0 and t = h you get 1/3Ah.\n\nThe volume of the prism is Ah.