Question 957568
s=length of all edges A=Area; V=volume; SA=surface area; a=altitude of triangular base
The altitude of the triangular base of the prism would be given by:
{{{a=(sqrt(3)/2)s}}}
The area of an equilateral triangle in terms of s (base=s) is:
{{{A[base]=(1/2)sa}}}
{{{A[base]=(1/2)s*(sqrt(3)/2)s}}}
{{{A[base]=(sqrt(3)/4)s^2}}}
So volume of the prism would be given by (height=s):
{{{V=A[base]*height}}}
{{{V=(sqrt(3)/4)s^3}}}
The surface area would be:
{{{2*A[base]}}}+Area of sides
Each side would have {{{Area=L*W=s*s=s^2}}}
The area of all 3 sides={{{3s^2}}}
.
And {{{2*A[base]=2(sqrt(3)/4)s^2}}}={{{(sqrt(3)/2)s^2}}}
.
{{{SA=((sqrt(3)/2)s^2)+3s^2}}}
.
{{{SA=(s^2)(sqrt(3)/2+3)}}}