Answer:
494.34 ft^2
Explanation:
If we assume the given ratio units are actual side lengths, then we can compute the area using Heron's formula:
A = √(s(s-a)(s-b)(s-c)) . . . . where a, b, c are side lengths, and s=(a+b+c)/2
For this triangle, that area is ...
s = (25 +14 +12)/2 = 51/2 = 25.5
A = √(25.5(25.5 -25)(25.5 -14)(25.5 -12)) = √(25.5·0.5·11.5·13.5) = √1979.4375
A ≈ 44.4909 . . . . square ratio units
__
The perimeter in ratio units is 2s = 51. The actual perimeter is 170 feet, so the scale factor between ratio units and feet is ...
(170 ft)/(51 ratio units) = (10/3) ft/ratio unit
The area scale factor is the square of this, so the area in square feet is ...
(44.4909 units^2)(10/3 ft/unit)^2 = 494.34 ft^2