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Question:I have a parcel with four sides with lengths of 111 on the north, 120 on the south, 83 on the west and 95 on the east. I do not know any of the angles and presume that none of them are right angles. Also presume that none of the sides are parallel to each other.
I can't divide it into two triangles and calculate those areas using the formula 1/2 b X h because neither of the triangles would have a right angle.
How do I go about calculating the area?
Answers:Use the Brahmagupta Formula, A = SqRt[(s-a)(s-b)(s-c)(s-d)], where a, b, c and d are the lengths of the four sides of the quadrilateral, and s = (a + b + c + d)/2.
s = (111 + 120 + 83 + 95)/2 = 204.5
Area = Square Root [(204.5 - 111)(204.5 - 120)(204.5 - 83)(204.5 - 95)] = Square Root [93.5 x 84.5 x 121.5 x 109.5] = SqRt [105,113,553.2] = 10,252.4901
Question:I know that to find out the distance travelled by, lets say a car, in a speed time graph, you have to measure the area beneath the line. However, if the acceleration is irregular before the car reaches constant speed and the deceleration is so irregular that it looks like a snake, then how do you actually calculate the distance travelled by the car? And also supposing that the area under the line of the speed-time graph isn't divisible by shapes...
Answers:Assuming that the graph is continuous, you integrate to find the area under the curve. Judging by the nature of your question, and your additional info, you haven't studied calculus. If the graph is a straight line, then you can easily form a rectangle, or a triangle. If the graph is a curve, then you can still form these rectangles, but they need to be much smaller. In fact, we make them infinitely small. Then we calculate the area of each rectangle and add them together. This is what the definite integral is made to do.
Question:I have a lake Satori map, and need to calculate the area of it, irregular shape, just given 1cm= 1 mile, and dont divide into small shapes to calculate. I think it does something with the calculus, but dont know how (no functions, just a picture, a ruler, that's all) Can you tell clealier?
Answers:If the shape is irregular, and you don't have formulas for the parts of that shape, the area can only be measured, not calculated. A suggested by another responder, a planimeter is used for this purpose--it is a mechanical device, and you trace the perimiter of the lake with a little wheel and you can read the area. You calibrate it by measuring a known area such as a 1cm square.
There are other approaches. You can cut out the shape of the lake (if you don't want to cut the map, you can trace the outline onto tracing paper and cut that out). Weigh the cut out piece and compare to the weight of a known area also cut out and weighed.
Question:I need to calculate the internal angles of an irregular polygon with 4 sides. I have the area, and the lengths of each side, but no way to accurately measure the diagonal or any interior angle. Is there a formula that will work? I need to calculate the internal angles of an irregular polygon with 4 sides. I have the area, and the lengths of each side, but no way to accurately measure the diagonal or any interior angle. Is there a formula that will work? NB The quadrilateral does satisfy Brahmagupta's formula. Correction the polygon doe NOT satisfy Brahmagupta's formula.
Thanks for helping all!
Answers:In general, this is not enough information. There may be more than one solution that gives the same area. If the quadrilateral can be inscribed in a circle, you should have a unique solution. It can be inscribed in a circle if the sides and area satisfy Brahmagupta's Formula (see http://en.wikipedia.org/wiki/Brahmagupta%27s_formula
Brahmagupta's formula - Wikipedia, the free encyclopedia )
Continued: OK. It can be inscribed in a circle. Draw the two diagonals. I don't know what course you're taking. There are several theorems that deal with the ratios of the segments of lines crossing in a circle. I am retired and no longer have the book I need to refer to for the solution to this one. Send me a note if you wish and I'll help you with it.
Area of Irregular Shapes :This video illustrates how to find the area of an irregular shape by breaking it down into familiar regular shapes, as required by high school geometry courses. For more instructional videos, as well as exercise and answer sheets, go to: freemathtutoring.googlepages.com
Area of Irregular Polygons :Watch as Mr. Almeida explains how to find the area of irregular polygons. The key to finding the correct is to use your parallel lines as key pieces of information. Also, some shapes not always be composed of quadrilaterals, some may be made up of triangles. This will impact which formula you use. If it is a rectangle, then you will use A=lw, but if it is a triangle, you will use the formula A=1/2 xbx h.