Results 1 to 3 of 3

Thread: need help, please!

  1. #1
    Newbie
    Joined
    Mar 2008
    Posts
    12

    Smile need help, please!

    1. In the examination figure the sides of the triangle b=501, c=392.6, d=512.8 find the area to the nearest 10 square feet
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    11,152
    Thanks
    731
    Awards
    1
    Quote Originally Posted by hamadouousmane View Post
    1. In the examination figure the sides of the triangle b=501, c=392.6, d=512.8 find the area to the nearest 10 square feet
    Do a search for Heron's formula.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Sep 2007
    Posts
    528
    Awards
    1
    Quote Originally Posted by hamadouousmane View Post
    1. In the examination figure the sides of the triangle b=501, c=392.6, d=512.8 find the area to the nearest 10 square feet
    There are two methods. I've showed both.

    ____________________

    1st method, Heron's Formula:

    $\displaystyle s = \frac{(a+b+c)}{2} = \frac{(501+392.6+512.8}{2} = 703.2$
    $\displaystyle a = \sqrt{(703.2)(703.2 - 501)(703.2 - 392.6)(703.2 - 512.8)} = 91700$ $\displaystyle \mathrm {units} ^2$

    ____________________

    2nd method, Geometry:
    EDIT: I have attached a diagram so you can see how it is geometrically.

    Find the height by using Pythagoras and then use the standard triangle area formula.
    $\displaystyle x^2 + h^2 = 501^2$ ---------(1)
    $\displaystyle (392.6 - x)^2 + h^2 = 512.8^2$ --------------(2)
    (2) - (1)
    $\displaystyle (392.6 - x)^2 - x^2 = 512.8^2 - 501^2 $
    Solve for $\displaystyle x$:
    $\displaystyle x = 181$
    Substitute $\displaystyle x$ value into formula (1) or (2) to get $\displaystyle h$.
    $\displaystyle h = 467$
    $\displaystyle \mathrm {Area} = \frac{1}{2}(\mathrm {Base})(\mathrm {Height}) = \frac{1}{2} (392.6)(467) = 91700$ $\displaystyle \mathrm {units} ^2$
    Attached Thumbnails Attached Thumbnails need help, please!-diagram.jpg  
    Last edited by Simplicity; Apr 4th 2008 at 11:16 AM. Reason: Attaching a diagram (Triangle Image) for 2nd method
    Follow Math Help Forum on Facebook and Google+


/mathhelpforum @mathhelpforum