What is the formula to find number of diagonals in an octagon?
964284
The question apparently is "How many diagonals does a polygon with n sides have?"  \n\nThe first formula is n(n-3)/2.  \nOne way to see this is to notice that you can draw (n-3) diagonals from every vertex of the polygon. This is because there are (n-1) other vertices, but two of them are adjacent vertices and so don't count towards making diagonals. This seems to give n(n-2) diagonals, but this way of counting counts every diagonal twice since each diagonal connects to two vertices, so you have to divide by 2.\n\nBy a recursive formula, we mean a way of expressing the answer for n vertices in terms of the answer for n-1 vertices. Suppose, for example, that you already know the answer for a polygon with n-1 vertices. Now if you add another vertex between two of the vertices of the original polygon, then all the diagonals of the original polygon will still be diagonals of the new polygon, and so will the side joining the two vertices that you added a new vertex between, and so will the line segments joining the new vertex to all the other vertices of the original polygon. (Got all that?) So if we let diag(n) be the number of diagonals for a polygon with n sides, we get the formula:\n\n        diag(n) = diag(n-1) + n - 3 + 1 or\n\n                  diag(n-1) + n - 2\n\nThe first formula is better, since it actually gives you the answer.  \nBut sometimes it's easier to get a recursive formula first and use \nthat to get an explicit formula (your first formula is an explicit one \nsince you only need the number of vertices in the polygon to get the number of diagonals in that polygon).  This is called "solving the recursion."  Sometimes a recursive formula is the best you can do because there simply is no explicit formula.\n\nI hope this helps.
515192
If it's a square, (60 x 60) then probably 8.\nIf it's a circle (r=60) then probably 10.\nIf it's a cirlce (d=60) then probably 6
623411
Pentagon = 5, decagon = 10, quadrilateral = 4, and heptagon = 7.
350015
No squares just  octagons!
309782
You are attempting to find the diagonal of a square with 5 on a side. The answer is obviously 5*√(2). C, the hypotenuse of a right triangle, is the longest side of the said triangle. Therefore, C must be larger than 5 in your particular problem. Hence, the first two answers are incorrect.\n\nExample:\nIn general, a square with sides of length x has a diagonal of length x*√(2).\n\na^2 + b^2 = c^2\nx^2 + x^2 = c^2\n2*x^2 = c^2\n√(2*x^2) = √(c^2)\n√(x^2)*√(2) = c\nx*√(2) = c\n\nIf x = 5, then c = 5*√(2).
901368
You need to take triangles with leg length 2-sqrt(2) from each corner. That is about 0.586".\n\nThe length of each side of the octagon will be 2 * sqrt(2) - 2. This is about 0.828"\n\nThis was calculated by setting the length of each leg of each triangle to x.\n\nhypotenuse = remaining side of square\n\nx * sqrt(2) = 2 - 2x. And then solve for x.
584072
I would use the trapezoid rule myself. For seven vertices:\nV0 = (x(0),y(0))\nV1 = (x(1),y(1))\nV2 = (x(2),y(2))\n...\nV6 = (x(6),y(6))\n\nFor notational convenience, define V7 = V0.\nThat is, x(7) = x(0) and y(7) = y(0).\n\nThen the area is:\n\n 6\nSUM ( x(i+1)*y(1) - x(i)*(y(i+1) ) / 2\ni=0\n\n= ( x(1)*y(0) - x(0)*y(1)\n + x(2)*y(1) - x(1)*y(2)\n + x(3)*y(2) - x(2)*y(3)\n + x(4)*y(3) - x(3)*y(4)\n + x(5)*y(4) - x(4)*y(5)\n + x(6)*y(5) - x(5)*y(6)\n + x(0)*y(6) - x(6)*y(0) ) / 2\n\n\nIf the heptagon is regular, you don't need to know the coordinates of the vertices, just the length of the regular side(s):\n\nA = (7/4) * s^2 * cot(π/7)
319863
It has to do woth the number of vertices of hexagons written inside other hexagons.  Go to \n\nhttp://mathworld.wolfram.com/HexagonalNumber.html\n\nfor more details.
726378
LW = A\n15W = 200\nw = 200/15 = 40/3\n\nThe diagonal will, along with one width leg and one length leg, form a right triangle.  Using the Pythagorean theorem, a^2 + b^2 = c^2, we can figure out the length of the diagonal:\n(15)^2 + (40/3)^2 = c^2\n225 + 8000/9 = c^2\n10025/9 = c^2\nc = (sqrt)(10025/9) = (sqrt 10025)/3 = 5(sqrt 401)/3
818330
Go to yahoo.com\n\nIn the search engine,  type in; \n\ndiagonal polygons +images\n\nYou will actually get images of diagonal polygons at that point!
496924
Well, you know that each corner of the octagon lies on the circle (by definition). So, if A and B are the names of two adjacent corners, and C the center of the circle, you also know that AC=14.15, and BC=14.15. \n\nAnd you also know that a regular octagon will have its corners equally spaced around the circle. Since a circle is 360 degrees, the AC/BC angle is 360/8 = 45 degrees.\n\nFrom there you can easily calculate the length of AB using simple trigonometry, which is probably the goal of the exercise :-)
871030
2x^2-8x+17=x^2+2x-7\n-->\nx^2-10x+24=0\nx^2-6x-4x+24=0\nx(x-6)-4(x-6)=0;\n(x-4)(x-6)=0\nx=4 or 6;\nSo the length of each diagonal is \n17 or 41
74297
(# sides - 2) * 180 = sum of all the interior angles\n\n[(# sides - 2) * 180]/(# sides) = each interior angle if they're all congruent
816720
area of rhombus=(1/2)d1d2\n(1/2)*16*d2=120\n8d2=120\ndividing by 8\nd2=120/8=15\nthe other diagonal is 15'
675746
by the number of sides and angles
63969
A hexagon has 6 sides.
878030
How to find the area of an octagon:\n\nMeaning of words\n\nAn octagon is a polygon having eight sides.\nA polygon is a closed plain figure bounded by three or more straight sides that meet in pairs in the same number of vertices and do not intersect other than at these vertices.\nVertices is the plural of vertex.\nVertex means the point opposite the base of a figure or the point of intersection of two sides of a plain figure or angle.\n\nDifferent methods or formulas are used for calculating the area of polygons. The following method is used for calculating the area of an octagon.\n\nFormula: 2 × r2× 1.4142135 (the last number is the square root of 2)\n\nr = radius\n\nThe radius is a straight line from the centre to any point on the outside of the shape.\n\nFind the radius of the octagon, then perform the formula.\ne.g. if the radius of an octagon was 4 cm, then 2 × 42× 1.4142135 = 45.25 cm2, which is the area.