Find the area of triangle PQR if PQ = QR = 12 and angle PQR = 120 degrees.
I assumed that the 120-degree angle is between the two equal sides.
Use the law of Cosines to find the 3rd side of the triangle:
Obtuse isosceles triangle.
Sides: a = 12 b = 12 c = 20.785
Area: T = 62.354
Perimeter: p = 44.785
Semiperimeter: s = 22.392
Angle ∠ A = α = 30° = 0.524 rad
Angle ∠ B = β = 30° = 0.524 rad
Angle ∠ C = γ = 120° = 2.094 rad
Height: ha = 10.392
Height: hb = 10.392
Height: hc = 6