Results 1 to 3 of 3

Math Help - Area of five-sided coin

  1. #1
    Newbie
    Joined
    Apr 2011
    Posts
    4

    Area of five-sided coin

    stuck on another problem from Abbott`s "Teach Yourself" Trigonometry:

    A new five-sided coin is to be made in the shape of figure /image attached/

    Тhe point А on the cirсumferenсe of the coin is the сentre of the
    arc CD, which has а radius of 2 сm. Similarly B is the сentre of
    the arс DЕ, and so on. Find the area of one faсe of the сoin.

    hope you can help me, thanks in advance!
    Attached Files Attached Files
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,806
    Thanks
    116
    Quote Originally Posted by dmi3 View Post
    stuck on another problem from Abbott`s "Teach Yourself" Trigonometry:

    A new five-sided coin is to be made in the shape of figure /image attached/

    Тhe point А on the cirсumferenсe of the coin is the сentre of the
    arc CD, which has а radius of 2 сm. Similarly B is the сentre of
    the arс DЕ, and so on. Find the area of one faсe of the сoin.

    hope you can help me, thanks in advance!
    1. Draw a sketch (see attachment)

    2. Draw a pentagon ABCDE. Determine the interior angles.

    3. The area of the coin consists of
    triangle
    • ACD: a_{ACD} = \frac12 \cdot 2 \cdot 2 \cdot \sin(36^\circ)
    • 2 triangles ABC: a_{ABC} = \frac12 \cdot 2 \cdot h = \tan(36^\circ)
    • 5 segments: area of sector - area of triangle ACD: a_{segm}= \frac{36^\circ}{360^\circ} \cdot \pi \cdot 2^2 - \frac12 \cdot 2 \cdot 2 \cdot \sin(36^\circ)


    4. I've got a_{coin} \approx 3.034\ cm^2
    Attached Files Attached Files
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2011
    Posts
    4
    3.034 is correct, thanks!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Calculating area 6 sided figure
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: October 2nd 2011, 11:07 PM
  2. Replies: 4
    Last Post: September 6th 2010, 03:04 AM
  3. 29-sided die
    Posted in the Statistics Forum
    Replies: 2
    Last Post: July 25th 2009, 07:48 PM
  4. Area of a crazy 5 sided figure
    Posted in the Geometry Forum
    Replies: 3
    Last Post: July 20th 2009, 10:24 PM
  5. Magic Coin Toss aka: 3 sided die
    Posted in the Statistics Forum
    Replies: 4
    Last Post: April 3rd 2009, 02:34 PM

Search Tags


/mathhelpforum @mathhelpforum