Question 1005087
<pre>
The rhombus looks like the figure below.  Since its perimeter 
is 120 ft., each equal length side is 120/4 = 30 ft.

{{{drawing(5000/23,400,-2.5,2.5,-4.6,4.6,
green(locate(-.1,0,40)),
line(-2,0,0,-sqrt(13)),

locate(1.2-.2,2.2,30),locate(-1.2-.2,2.2,30),locate(-1.2-.3,-1.2-.3,30), locate(1.2-.1,-1.2-.3,30),


line(-2,0,0,sqrt(13)),
line(2,0,0,sqrt(13)),green(line(-2,0,2,0)),
line(2,0,0,-sqrt(13)) )}}}

We draw the other diagonal in red, which bisects the 
green 40 ft. diagonal into two 20 ft. line segments.

{{{drawing(5000/23,400,-2.5,2.5,-4.6,4.6,
green(locate(-1,0,20),locate(.8,0,20)),
line(-2,0,0,-sqrt(13)),

locate(1.2-.2,2.2,30),locate(-1.2-.2,2.2,30),locate(-1.2-.3,-1.2-.3,30), locate(1.2-.1,-1.2-.3,30),
red(line(0,-sqrt(13),0,sqrt(13))), 

line(-2,0,0,sqrt(13)),
line(2,0,0,sqrt(13)),green(line(-2,0,2,0)),
line(2,0,0,-sqrt(13)) )}}}

So the rhombus consists of 4 right triangles, so we
find the area of one of them and multiply by 4. Here is
just one of them:

{{{drawing(5000/23,400,-2.5,2.5,-4.6,4.6,
green(locate(-1,0,20)),


locate(-1.2-.2,2.2,30),
red(line(0,0,0,sqrt(13))), 

line(-2,0,0,sqrt(13)),
green(line(-2,0,0,0)) )}}}

We use the Pythagorean theorem to find its height,
We know its base is b=20 and its hypotenuse is 30,
we find a, the green height:

{{{a^2+b^2=c^2}}}
{{{a^2+20^2=30^2}}}
{{{a^2+b^2=900}}}
{{{a^2=500}}}
{{{a=sqrt(500)}}}
{{{a=sqrt(100*5)}}}
{{{a=10sqrt(5)}}}

The area of the above right triangle is given by 
the formula:

{{{A=expr(1/2)*base*height}}}
{{{A=expr(1/2)*20*10sqrt(5)}}}
{{{A=100sqrt(5)}}}

So the area of the rhombus is 4 times that or

answer = {{{400sqrt(5)}}}, or about 894.427191 sq. ft.

Edwin</pre>