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Math Help - geometry help

  1. #1
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    geometry help

    I need help with a couple geometry problems that i am having trouble with. The first one involves a semi-circle with 2 congruent semi-circles inside of it and i am suppose to find the area of the shaded region given that the diameter of the large semi-circle is 9.2 cm. The second question is a square with s4 circles incribed in it. i am given that the sides of the square are 12.4 cm. For the sqaure question, i could not figure out the radius of the circles inside so that i could use it to subtract it from the area of the square.
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  2. #2
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    [size=3]Hello, ogglock!


    1) Given a semicircle with 2 congruent semicircles inside of it.
    The diameter of the large semicircle is 9.2 cm.
    Find the area of the shaded region.
    Code:
               ..* * *..
              *:::::::::::*
            *:::::::::::::::*
           *:::::::::::::::::*
           :::* *:::::::* *:::
          **       *:*       **
          * - -+- - * - -+- - *
          : - 4.6 - : 2.3: 2.3:
          : - - -  9.2  - - - :

    The radius of the large semicircle is 4.6 cm.
    The radii of the small semicircles is 2.3 cm.

    Can you find the difference of the areas?




    Given a square with side 12.4 cm.
    Four congruent circles are inscribed in the square.
    Find the area of the shaded region.
    Code:
          : - - - -  12.4  - - - - :
          *---*-*-*-------*-*-*---*
          |:*       *:::*       *:|
          |*         *:*         *| 
          |                       | 
          *     +     *     +     *
          |                       | 
          |*         *:*         *| 
          |:*       *:::*       *:| 
          |:::* * *:::::::* * *:::|
          |:*       *:::*       *:|
          |*         *:*         *|
          |                       |
          *     +     *     +     * 
          |                       |
          |*         *:*         *|
          |:*       *:::*       *:|
          *---*-*-*-------*-*-*---*
          : 3.1 : 3.1 : 3.1 : 3.1 :

    The side of the square is 12.4 cm.

    Can't you see that the radius of the circles is 3.1 cm?

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  3. #3
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    Drafting programs

    I see that Soroban has given you some nice diagrams to assist you ...and gave you some good hints, letting you complete the problem. How far did you get with it?

    Soroban: If using a PC, I found that DeltaCad is one of the best, simplest, most intuitive drafting programs around. Presently I'm using an Apple iMac as well as a PC laptop. The diagram here was done using the HighDesign architectural drafting program. Unfortunately, neither is free. HighDesign is an excellent program, but a bit over the top for simple geometric drawings such as this, and I far prefer DeltaCad for this purpose. However, this takes only a few seconds with practice due to use ...

    P.S. Any hints on what program to use for the Apple iMac to send symbolic algebra here would be appreciated.
    Attached Thumbnails Attached Thumbnails geometry help-circles.jpg  
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  4. #4
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    I would like to thank you guys for the help you have given me so far. After doing the questions, i got 99.7 for the semi circle question which i got from taking the area of the large semi-circle which was 132.9 and subtracted it from the area of the congrugent circles which was 16.62*2 because there were two semi-circles. The second question i got 33.0 from taking the area of the square which was 153.76 and subtracted it from the area of the circles which was 30.19*4. I think these answers are right but i am not sure.
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  5. #5
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    bump
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  6. #6
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    I don't match that. You might check your formulas for area, your application of that formula, and your arithmetic. I'll do the same, of course.
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  7. #7
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    Quote Originally Posted by Diagonal View Post
    I don't match that. You might check your formulas for area, your application of that formula, and your arithmetic. I'll do the same, of course.
    I don't see any problems with my arithmetic in doing the question. Can you check if i did it right if not either correct me or show me what you did.

    EDIT: i know what i did wrong with the semi-circle question, i used the whole circle formula instead of the semi-circle one

    For the question with the semi circles i used 1/2pi r^2 to find the area of the large semi-circle which was 33.238. I then used that same formula to find the area of the congruent semi-circles which was 8.310 but multiplied it by 2 as there were 2 semi-circles inscribed. So my final calculation was 33.238-16.619 which got me 16.619.

    For the question with the 4 inscribed circles, i first found the area of the square by taking the sides of it and squaring it(12.4^2=153.76). i then used the pi r^2 formula to find the area of the circle which was 30.19 then multiplied it by 4 because there were 4 circles inside of the square(30.19*4=120.76). To find the area of the shaded i subtracted the two values (153.76-120.76) and got 33
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  8. #8
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    bump did the answers i got match up with someone elses?
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