Results 1 to 3 of 3

Math Help - Shaded area

  1. #1
    Newbie
    Joined
    Apr 2014
    From
    United Kingdom
    Posts
    17

    Shaded area


    I was discussing this question with my friends but we're all disagreeing...

    Here's what I started with:
    If you draw bisectors from each of the vertices of the inner triangle (enclosing circle with r), the vertical line will be split into a 2:1 ratio, which is 2r:r
    Is this the right way to start?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor ebaines's Avatar
    Joined
    Jun 2008
    From
    Illinois
    Posts
    1,153
    Thanks
    348

    Re: Shaded area

    I would start by calculating the area of the inner triangle. It's height is 2R (as you note it's 2R from the center to the top vertice, plus 1r from the center to the base), and its base is 2 r \sqrt 3 - do you see why that is? Next find the radius of the larger circle - oh wait, we've already determined that it's 2R - and determine its area. Finally find the height and base of the large triangle so you can determine its area. Then the shaded area is:

     Area = A_{Large\ T} - A_{Large \ C} + A_{Small\ T} - A_{Small \ C}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Nov 2010
    Posts
    1,932
    Thanks
    782

    Re: Shaded area

    Yes, you started correctly.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Shaded area
    Posted in the Calculus Forum
    Replies: 5
    Last Post: March 11th 2014, 08:52 AM
  2. area of the shaded area of the circle.
    Posted in the Geometry Forum
    Replies: 4
    Last Post: October 23rd 2010, 02:37 PM
  3. area of shaded
    Posted in the Geometry Forum
    Replies: 4
    Last Post: October 10th 2009, 04:57 AM
  4. Area of shaded region
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 7th 2008, 08:02 PM
  5. find area of shaded area (yellow)
    Posted in the Geometry Forum
    Replies: 8
    Last Post: September 4th 2007, 09:34 AM

Search Tags


/mathhelpforum @mathhelpforum