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Pre-Calculus - Regarding finding the area of a certain region

  1. Apr 1, 2005 #1
    URGENT: Regarding finding the area of a certain region within a circle

    Hello

    I have included an image of the diagram with the question on it. I understand what I am trying to find here is the sector of the circle, however to calculate this you must have the radius of the circle... something which this certain problem does not give. Can someone please lead me in the correct direction to solving this problem... thanks.

    edit: perhaps I have made some progress... if I make the outer regions a triangle (therefore creating 4 segments and 4 triangles of course), is it possible for me to just simply find the area of the triangle and then find the area of the segment then add these togeather to find the total area? I am not so sure as to how I find the area of a segment in this particular problem since in order to find the area of a segment, you must have the radius. I am not sure if I am able to just calculate this by using 3 as the radius. Here is what I have so far, but I am not so sure this is correct.

    K(area) = (1/2)(3)(3)sin60
    K(area) = 3.897114317
    then after calculating the area of the triangle, I go on to calculate the segment by
    A (area of segment) = (1/2)3^2((pi/180)(60)-sin60))
    A = .8152746634

    Now for the total area of one side I would add K + A to get 4.71238898. I would go on to multiply this by 4 to find the total area of the shaded region. I am very skeptical about the way I tried to solve this.
     

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    Last edited: Apr 1, 2005
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  3. Apr 1, 2005 #2

    HallsofIvy

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    Question: Is the little cap at the end of each leg of the cross included in the shaded region? It doesn't look like it is shaded in the picture, but I assume the problem is to find the area of the circle that is NOT included in the cross. In that case, the simplest way to do the problem is NOT to find the area of each little section separately. Find the area of the circle, the area of the cross (made of rectangles) and subtract.
     
  4. Apr 1, 2005 #3
    Hrm, hadn't thought of it that way. But how should I go about finding the area of the circle? I don't have the radius or the circumference, all I have are the values for the equilateral cross. Also, those caps are not shaded, only the sectors.

    The only part I am iffy about it in the way I approached the problem is my calculation for the segment, I am not sure if I am able to just use the value of 3 as the radius for the calculation. I don't know how I would derive the radius with only the values of the equilateral cross, this is the only part throwing me off.
     
    Last edited: Apr 1, 2005
  5. Apr 1, 2005 #4
    Problem has been figured out... alls I had to do was simply being togeather the shaded regions to create a smaller circle with the diameter of 6. Thanks for anyone who attempted to help!
     
  6. Apr 1, 2005 #5
    the R of the circle = sqrt[90]/2
     
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