Question 314450
{{{drawing(300,300,-10,10,-10,10,line(-6.5,0,0,5),line(0,5,6.5,0),line(6.5,0,0,-5),locate(-3,0,b/2),line(-1,1,0,1),line(-1,0,-1,1),locate(0.5,3,h/2),locate(-3.5,4,x),line(0,-5,-6.5,0), blue(line(-6.5,0,6.5,0)),blue(line(0,-5,0,5)))}}}
I'm assuming by height and base you mean the measures of the diagonals.
{{{A=(1/2)(10)(13)=65}}}
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Find the length of the side using {{{b/2}}} and  {{{h/2}}}  and the Pythagorean theorem,
{{{x^2=b^2/4+h^2/4=100/4+169/4=269/4}}}
{{{x=sqrt(269)/2}}}
{{{P=4x=2*sqrt(269)}}}