Question 1206859
<pre>

{{{drawing(1.3*3200/11,1.3*400,-5,3,-2,9,

red(arc(-1,6,8.5,-9.5,261,270)),

locate(-1.53,2,36^o),

line(-4,1,-2,-1),
line(-2,-1,2,-1),
line(2,-1,0,1),
line(0,1,-4,1),
line(-4,1,-1,6),
line(-2,-1,-1,6),
line(2,-1,-1,6),
line(0,1,-1,6),
green(line(-1,0,-1,6)),

line(-2,-1,0,1),
locate(-4-.2,1,A), locate(-2,-1,B), locate(2,-1,C), locate(-.1,.9,D), locate(-1,6.5,F), 
locate(-1,0,K) ,  locate(-1.4,-.4,5)


 )}}}

First find the area of triangle BFK, half of triangle BFD.

BD=10, so BK=5

{{{BK/(FK)=tan(36^o)}}}

{{{5/(FK)=tan(36^o)}}}

{{{Fk*tan(36^o)=5}}}

{{{FK=5/tan(36^o)}}}

{{{matrix(1,4,AREA,OF,DELTA,BFK)}}}{{{""=""}}}{{{expr(1/2)BK*FK}}}{{{""=""}}}{{{expr(1/2)*5*(5/tan(36^o))}}}{{{""=""}}}{{{25/(2tan(36^o))}}}

{{{matrix(1,4,AREA,OF,DELTA,BFD)}}}{{{""=""}}}{{{25/(tan(36^o))}}}{{{""=""}}}{{{matrix(1,2,34.40954801,cm^2)}}}

To find the perimeter, we need to find FB.

{{{BD/(FB)=sin(36^o)}}}

{{{5/(FB)=sin(36^o)}}}

{{{FB*sin(36^o)=5}}}

{{{FB=5/sin(36^o)=8.506508084=FD}}}

{{{matrix(1,4,AREA,OF,DELTA,BFD)}}}{{{""=""}}}{{{25/(tan(36^o))}}}{{{""=""}}}{{{matrix(1,2,34.40954801,cm^2)}}}


{{{matrix(1,2,34.40954801,cm^2)}}}

{{{matrix(1,4,PERIMETER,OF,DELTA,BFD)}}}{{{""=""}}}{{{FB+BD+FD}}}{{{""=""}}}{{{8.506508084+10+8.506508084}}}{{{""=""}}}{{{matrix(1,2,27.01301617,cm)}}}.

Rounding off to the nearest integer:

{{{matrix(1,4,AREA,OF,DELTA,BFD)}}}{{{""=""}}}{{{matrix(1,2,34,cm^2)}}}

{{{matrix(1,4,PERIMETER,OF,DELTA,BFD)}}}{{{""=""}}}{{{matrix(1,2,27,cm)}}}.

Edwin</pre>