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



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



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:



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:









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





So the area of the rhombus is 4 times that or

answer = , or about 894.427191 sq. ft.

Edwin