Rate of change of the area of a triangle

Calculus Level 4

In triangle ABC, \text{ABC}, AB=2\overline{\text{AB}}=2 and BC+CA=2AB.\overline{\text{BC}}+\overline{\text{CA}}=2\overline{\text{AB}}. Let B=θ\angle \text{B}=\theta and suppose that the rate of change of the angle θ\theta with respect to time is dθdt=2 (rad/sec).\frac{d\theta}{dt}=2\ (\text{rad/sec}).

Then, if SS is the area of the triangle, what is the rate of change of SS with respect to time when A=π2? \angle \text{A}=\frac{\pi}{2}?

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