i need to know the formulas for finding the area of a figure originated for a report and cant find anything?
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The first area to be defined was the obvious one of a rectangle.  The number of squares of unit size that would fill up a rectangle is clearly the number of such squares that fit in a row across one dimension of the rectangle, times the number of such rows needed.  Since each square has a length and width of one unit, it's easy to see that the length x width = area of a rectangle.\n\nA rectangle can be divided into two right triangles of equal size.  Hence, the area of a right triangle is 1/2 x length x width, only in triangles we call those things base and height.  Now, any arbitrary triangle can be broken up into two right triangles.  Doing so, it's easy to show that the area of *any* triangle is 1/2 x base x height, where the height is defined as the perpendicular distance from the line containing the base to the opposite vertex.  Similar techniques using triangles can be used to find the area of other regular polygons. \n\nThe area of things like circles can be computed from integral calculus, although I suspect there is probably a geometric method to find the area of a circle as well.\n\nThe area of figures bounded by more complex functions than straight lines and circles is found using integral calculus.
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If you have the equation of the curve then integrate it on the lower and upper limits of the variable. In some cases you can find devide the identical parts and find out area of a single identical part and multiply by the number of parts made (sine wave).\n\nIf shape is a simple square circle etc you can find area by simple formula.
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The aswer to this question is really quite easy. \n\nSince we know that the shaded area is a square, finding its area is a simple matter.  Its area is s^2, or s squared, where s is the length of one edge of the square.\n\nTo find the area of the circle, we use the fact that for any circle, its area is  A = pi x r^2, or pi times r squared, where r is the radius of the circle.  To find a circle's radius, measure from the circle's center to any point on the circumference of the circle.  Multiply r by itself.  Then multiply that result by pi.  That gets you the area of the circle.\n\nWhat you seem to be looking for is the shaded area of the square remaining after removing the area of the circle.  To do this, simply subtract the area of the circle from the area of the square.\n\nYour formula should look something like this:\n\nA (shaded) =  A (square) - A (circle) \n                   =  s^2 - (pi x r^2)\n\nNotice that it does contain the constant pi.\n\nIf your circle is tangent to all sides of the square in which it is inscribed  (a single point on the circumference of the circle touches each side of the square at its mid-point), then your job is made easier still.\n\nA circle tangent to a circumsribed square (in this case a square constructed outside of the circle) has a radius equal to half the length of a side of the square.\n\nThen the above formula collapses to:\n\nA (shaded) = s^2 - (pi x (s/2)^2)\n                   = s^2 - (pi x (s^2/4))\n                   \nNote s^2/4 is read s squared divided by four.\n\nFactoring out common factors, we get \n\nA (shaded) =  s^2  x  (1)  -  s^2  (pi/4)             \n                   =  s^2  x  (1 - pi/4)\n\nNote that pi/4 is less than 1, so (1 - pi/4) is a positive number.\n\nHope this helps.
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rare gem's answer is right..given the radius you'll just need to compute for the area using the formula right?\n\nArea=(radius^2)(pi)\n    = (5)(5)(pi)
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For a trapezoid? its a 2D figure so there are only area and perimeter.  Area is A= 1/2(base1 + base2)height or A= ((base1 + base2)height)/2
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if u kno the base and height.. then area= (base x height)/2\n\nif the triangle is scalar,\nthen :\n\nfirst find s, using hero's formula\n\ns= (a+b+c)/2   .... where a,b,c are the sides of triangle.\n\nthen , area = squareroot(s x (s-a) x (s-b) x (s-c)
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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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volume = (1/3) b h = 1/3 pi r 2 h \nSurface area = pr2 + prs\ns= the height of the outside of the cone, while h = the height of the cone at its center
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Area of rectangle = length x width \nArea of a circle = pi x R x R = pi R^2 where pi~3.14 and R - radius\nArea of an ellipse = pi x a x b see http://www.tpub.com/content/engineering/14069/css/14069_33.htm \n\nVolume = area of the base times hight\nVolume of a rectangular prism= area of rectangle x height = length x width x height\nVolume of a sphere = (4/3)pi x R x R x R = (4/3)pi x R^3\n \nCheck math tables or the web for equation of other geometric figures \n\nPercentage = 100 x (partial amount) / (total amount)\n\nHave fun
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Area of a Rectangle\nA rectangle is a good, simple shape to begin with. The area of a rectangle is equal to the product of the length of its base and the length of its height. The height is a segment that is perpendicular to the base. For a rectangle, the base and height are often called the "length" and the "width", and sometimes the height is referred to as the "altitude." \n\nArea of a Parallelogram\nTo find the area of a parallelogram, we can use the same formula that we used for the area of a rectangle, multiplying the length of the base times the length of the height. \n\n\n\nLet's find the area of a parallelogram that has a base of 23 cm and a height of 7 cm. If we substitute the values into the formula, we find that the parallelogram has an area of 161 square centimeters\n\n&...
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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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This is a lot to ask here. Why dont you look it up? \n\nAnd a lot of these are easy to figure out. \n\nSphere surface area is A=4 *pi *R^2 where R is the radius\n\nbecause A={int 0 to 2 pi} {int 0 t0 pi} R^2 sin(a)dadb\n\n\nThe cube surface area is A=6*S^2, where S is the length of an edge because there are 6 sides, each of area A^2.\n\nThe cylinder surface area A=2*pi*(R^2)+2*pi*R*H, where R is radius and H is height, because it has two circular end caps of area pi*(R^2) and a side of dimensions 2*pi*R by H, when it is unrolled. \n\nCone surface areas can be found the same way. Just unroll the side, and you get a triangle with height sqrt(H^2+R^2) and base 2*pi*R. The area of a triangle is .5*base*height. Then add in the area of the round bottom. \n\nAnd so on. I am sure you can do this yourself.
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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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area = r^2 * pi\narea = 9.8^2 * 3.1415\narea = 96.04 * 3.1415\narea is about 301.71
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Surface Area = 4*PI*r^2\n\nr = SQRT(SA/4/PI)
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Surface Area = [Base Area] +\n1/2 × Perimeter × [Side Length]\n\nVolume = 1/3 × [Base Area] × Height\n\nThe Surface Area has two parts: the area of the sides (the Lateral Area) and the area of the base (the Base Area). \n\nThe Base Area depends on the shape, there are different formulas for triangle, square, etc. \n\nBut the Lateral Area is surprisingly simple. Just multiply the perimeter by the side length and divide by 2. This is because the sides are always triangles and the triangle formula is base times height divided by 2
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Area is given in square ft: Length * Width yields ft*ft=ft^2 =sqft\n\nVolume is given in cubic ft: L*W*Height yields ft*ft*ft=ft^3 =cuft\n\nThe formulas above are for area of a square or rectangle, and volume of these shapes in 3-dimensions.  \nFormulas for Area and Volume are different for circles, spheres, cylinders and such.\n\nArea of a circle = pi*(radius^2)\nVol of a sphere= (4/3)*pi*radius^3\nVol of a cylinder= pi*radius^2*Length