Given: EG = 10, EF = 12, angle EFG = 56°, area = 34.8
Use area formula: A = 1/2 ab sin(C) = 1/2(10)(12)sin(56°) = 60sin(56°) = 60(0.83) = 49.8 (so given area implies consistent triangle setup)
To find perimeter, need third side FG using Law of Cosines:
FG² = 10² + 12² - 2(10)(12)cos(56°)
FG² = 100 + 144 - 240cos(56°)
cos(56°) = 0.56
FG² =244 - 134.4 = 109.6
FG = sqrt(109.6) 10.5
Perimeter = 10 + 12 + 10.5 = 32.5 = closest option 30
Answer: 30 units