Results 1 to 7 of 7

Math Help - Area - composite shapes

  1. #1
    Newbie
    Joined
    Aug 2007
    Posts
    11

    Area - composite shapes

    For this question (see image) we are supposed to find the area of the shaded (blue) area of this shape. I know that I can work out the entire area of this shape using the area formula for a kite. How can I work out the area of the white part, though?

    Thanks in advance.
    Attached Thumbnails Attached Thumbnails Area - composite shapes-mathsquestion.gif  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,685
    Thanks
    616
    Hello, starship!

    If we don't know exactly what kind of curve that is,
    . . there is no way to calculate the area of the blue region.


    However, I do have a suspicion . . .

    Is that a right circular cone (a three-dimensional solid)?
    . . And we are asked to find its lateral area?

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Aug 2007
    Posts
    11
    I am assuming that it is just a two-dimensional shape as all of the other shapes I had to do were two-dimensional.

    I checked the answer sheet, and the area of the blue part is 163cm. The only problem is finding a way to end up with that answer.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by starship View Post
    I am assuming that it is just a two-dimensional shape as all of the other shapes I had to do were two-dimensional.

    I checked the answer sheet, and the area of the blue part is 163cm. The only problem is finding a way to end up with that answer.
    There is no way without knowing what the curve at the base of the shape is,
    and even then it will be a nasty calculation if it is what I think it is.

    RonL
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    Quote Originally Posted by starship View Post
    For this question (see image) we are supposed to find the area of the shaded (blue) area of this shape. I know that I can work out the entire area of this shape using the area formula for a kite. How can I work out the area of the white part, though?

    Thanks in advance.
    Let us say the arc is circular. So the unshaded area is that of a sector of a cirlce whose central angle is 50 degrees, and whose circle's radius is 17.75 cm.
    The area of the sector is the sum of the areas of the isosceles triangle and the secant of the circle. So, the area of the secant is area of sector minus area of isosceles triangle.

    Area of sector, A1 = (1/2)(radius)(arc) = (1/2)(radius)(radius*central angle in radians)
    A1 = (1/2)(17.75)[(50(pi/180))(17.75)]
    A1 = 137.47 sq.cm

    Area of isosceles triangle, A2 = "(1/2)(ab)sinC" = (1/2)(17.75)(17.75)sin(50)
    A2 = 120.66 sq.cm.

    So, Area of secant = A1 -A2 = 16.81 sq.cm.

    --------------
    The isosceles triangle containing the shaded area.

    Height of apex based from the chord of the sector is (40 minus the height of the apex of the unshaded isosceles triangle based on the same chord).
    H = 40 -17.75cos(25degrees) = 23.913 cm.

    Area of isosceles triangle containing the shaded area, A3 = "(1/2)(base)(height)"
    A3 = (1/2)(15)(23.913) = 179.35 sq.cm.

    Therefore, shaded blue area = 179.35 -16.81 = 162.54 sq.cm. -------answer.

    -------------
    Another way of finding the A2 is by the A = (1/2)(base)(altitude) also.

    Altitude of unshaded isosceles triangle, h = 17.75cos(25deg) = 16.087cm
    So, A2 = (1/2)(15)(16.087) = 120.65 sq.cm.

    Another way of finding h is by using the Pythagorean theorem,
    (17.75)^2 = (15/2)^2 +h^2
    h = sqrt[(17.75)^2 -(7.5)^2) = 16.088 cm.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Aug 2007
    Posts
    11
    Thanks, ticbol! It's making sense now.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Aug 2007
    Posts
    11
    I actually found an easier way of doing it, but you sent me down the right track.

    I worked out the entire area of the shape using the area formula for a kite and then subtracted the area of the sector:

    Area of kite = 15*40/2
    = 300cm

    Area of sector = (50/360)*pi*17.75

    = 137.47
    cm (rounded to two dp)

    Area of shaded area = 300 - 137.47
    = 162.53
    cm
    = 163
    cm
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: October 20th 2011, 03:22 PM
  2. Area of shapes?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 13th 2010, 07:30 PM
  3. Area allocation with shapes
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 13th 2009, 01:32 PM
  4. Different shapes with equal area
    Posted in the Geometry Forum
    Replies: 4
    Last Post: June 24th 2009, 12:23 AM
  5. urgent help with area of shapes
    Posted in the Geometry Forum
    Replies: 8
    Last Post: October 27th 2008, 05:42 AM

Search Tags


/mathhelpforum @mathhelpforum