Let x be the angle opposite to 12 and 10.
Smaller side be a
Larger side be b
The perimeter is 2a + 2b = 176, so a + b = 88.
Since Sin x = 10/a and Sin x = 12/b
12/b = 10/a
12a = 10b
a = 5b/6
Thus, a + b = 88
5b/6 + b = 88
11b/6 = 88
b/6 = 8
b = 48
10 is the altitude since it's perpendicular to a base.
Therfore Area = (10)(48) = 480 sq. units