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Geometry problem.

  1. Jul 22, 2005 #1
    I need to find the mid point of the area of the shape described below. This would divide the area into 4 subparts of equal area.. The dimensions of the shape are: north side is 300 feet, east side is 5000 feet, south side is 1500 feet, west side is 5142 feet. The south side is perpendicular to the east side.
     
  2. jcsd
  3. Jul 22, 2005 #2

    AKG

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    Draw a picture of it first. Now pick some arbitrary point on the east side, and draw a horizontal line there. Also draw a horizontal line at the lower of the two top points. You'll end up with a triangle on top of a trapezoid on top of another trapezoid. Let's say that the point you picked arbitrarily on the east side is x feet above the south side. Then you should be able to get an expression in terms of x for the area of the trapezoid below, and the trapezoid above. The area of the triangle will remain fixed. You want to solve for x such that the area of the bottom trapezoid is equal to the sum of the areas of the top trapezoid and the top triangle. Of course, you'll need to apply some basic trigonometry and geometry to find these areas in terms of x, and some basic algebra to solve for x. Do a similar thing picking an arbitrary point y on the south side, so the area to the left is equal to the area to the right. Upon picking an arbitrary point, you might find the shapes to the left and right are weird, so add lines so that you can break them up into simple shapes like trapezoids and triangles. Compute the left and right areas in terms of y and solve for y such that the areas are equal. Then the line at horizontal line at x and the vertical line at y will meet at the centroid.
     
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