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Homework Help: Some geometry

  1. Apr 29, 2007 #1
    1. The problem statement, all variables and given/known data
    Find the blue colored surface area.
    1 http://img338.imageshack.us/img338/1630/graph1zd7.png [Broken]
    The radii of the circles are 3 cm and 1 cm.

    2 Find the surface area of the rosette inside the equilateral triangle with side a.
    http://img87.imageshack.us/img87/2590/graph2dj9.png [Broken]

    2. Relevant equations

    3. The attempt at a solution
    I have no idea what to do with the first one.

    For the 2nd one the area of the rosette inside the triangle should be the area of 3 segments minus the area of the triangle.
    Here's a picture of what I did, with one circle only:
    http://img339.imageshack.us/img339/4650/circlerd9.png [Broken]
    This is what I got: [tex] \frac{a^2}{6}(2 \pi - \frac{3 \sqrt {3} }{2}) [/tex]
    But the book says it's [tex] \frac{a^2}{6}(2 \pi - 3 \sqrt {3} ) [/tex], so can anyone check it?
    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Apr 29, 2007 #2

    Gib Z

    User Avatar
    Homework Helper

    Precalc? I have no idea on the 2nd one, the first one you have you do a few things.

    First develop an expression for the area of the quadrilateral using Herons Formula for triangles generalized, i cant rememeber the precise name.

    [tex]A=\sqrt{(s-a)(s-b)(s-c)(s-d)}[/tex] where S = a+b+c+d, a b c and d are the lengths of the sides.

    Then draw a line from A to B and A to C. Use the cosine rule to find an expression for the angles at 01 and 02. Using those angles, you can see how much of the circles area it encompasses. Now find the area of the sectors and subtract from the rectangle.

    You won't get a very nice answer.

    For then 2nd one, what is it that you want us to check? It isnt very clear.
  4. Apr 29, 2007 #3
    Hey, thanks for your reply.
    I had another go at the 1st problem and I solved it, got the same answer as the book. I did differently than you, though, using the congruence theorem and some trig.

    Oh and there's a tiny difference between mine and the book's answer for the 2nd problem, just wanted to check who is right..
    Thanks again!
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