Results 1 to 2 of 2

Thread: Area

  1. #1
    Junior Member
    Jun 2010


    What might be the dimensions 0f a pentagonal prism if its surface area is 180cm
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Aug 2008
    The surface area of a regular pentagonal prism is given by

    $\displaystyle TSA = 2A_{\textrm{pentagon}} + 5lh$, where $\displaystyle l$ is one of the side lengths and $\displaystyle h$ is the height.

    The area of a regular polygon is given by

    $\displaystyle A = \frac{l^2n}{4\tan{\frac{\pi}{n}}}$, where $\displaystyle n$ is the number of sides, so the pentagon's area is

    $\displaystyle \frac{5l^2}{4\tan{\frac{\pi}{5}}}$

    $\displaystyle = \frac{5l^2}{4\sqrt{5-2\sqrt{5}}}$.


    $\displaystyle TSA = 2\left(\frac{5l^2}{4\sqrt{5-2\sqrt{5}}}\right) + 5lh$

    $\displaystyle = \frac{5l^2}{2\sqrt{5 - 2\sqrt{5}}} + 5lh$.

    Choose some values of $\displaystyle l$ and $\displaystyle h$ which will make this value $\displaystyle 180\,\textrm{cm}^2$.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. area-preserving maps between regions of equal area
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: Aug 23rd 2010, 08:33 PM
  2. Replies: 3
    Last Post: May 25th 2010, 12:01 AM
  3. Lateral Area and Total Surface Area
    Posted in the Geometry Forum
    Replies: 1
    Last Post: May 25th 2009, 04:28 PM
  4. Replies: 2
    Last Post: Nov 10th 2008, 09:27 AM
  5. Replies: 4
    Last Post: Apr 20th 2008, 07:03 PM

Search Tags

/mathhelpforum @mathhelpforum