The rate of change in area of a triangle having sides 10 cm and 12 cm when the variable angle between them is $\theta= 60°$, is :

$30 ~cm^2 /$ radian

x = 10 cm

y = 12 cm

θ = 60°

x, y → constant

θ → variable using concept of vectors

|Area| = $\frac{xy \sin \theta}{2}$  (magnitude of area)

so  $\frac{d A}{d \theta}=\frac{x y \cos \theta}{2}=\frac{10 \times 12 \times \cos 60}{2}$

$\Rightarrow \frac{10 \times 12}{2} \times \frac{1}{2}=\frac{30 ~cm^2}{rad}$