Expert: Azeem Hussain - 4/14/2009

Question
I don't understand how to find the lateral area for regular prism. Can you explain in steps how do i find the lateral area?

Answer
Hi Joe!

A regular prism has 6 faces, all of which are rectangles.  I'll ask you to draw a rectangular prism(ideally one where all the 3 dimensions look different).  Label the dimensions l, w, and h for length, width, and height.  Ensure every edge is labelled.  Now look at each rectangular face independently of every other.  You know the area of a rectangle is the product of its two dimensions, which are clearly labelled in your diagram right now.  Find the areas of the all the rectangles and add them together.  You should end up with:
A=lw+lw+wh+wh+lh+lh
A=2(lw+lh+lw)

Another way of thinking about it would be this.  Look at the prism as having 2 bases and a long "mural" bridging the two.  This mural is a long rectangle, whose height is that of the prism and whose length is the base perimeter of the rectangle.  That makes (2l+2w)h.  You must know account for the bases, which are the product of the non-height dimensions.  You have 2 of them, so 2lw.  Adding all this together:
A=(2l+2w)h+2lw
A=2(lh+wh)+2lw
A=2(lh+wh+lw)

Thanks for asking,
Azeem