Answer
$$78t^2+40t$$
Work Step by Step
We know the following equation for the area of the shaded region:
$$ A_{shaded}=\text{Overall Area} - \text{ Area Not Shaded}$$
Using this, we find:
$$ A=(21t+8)(4t)-(2t(3t-4)) \\ 84t^2+32t-6t^2+8t\\ 78t^2+40t$$