Answer: B

Video solution:

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Written solution:

Since $\angle BCD$ is a right angle, we can apply the Pythagorean theorem to $\triangle BCD$ to get that $\overline{BD} = 5.$ We also get that $\angle DBA$ is right since the sides of $\triangle BDA$ form a Pythagorean triple.

Then the area of $ABCD$ is equal to $$\begin{align*} \text{area}(\triangle &BDA) - \text{area}(\triangle BCD) \\ &= \dfrac{1}{2} \cdot 12 \cdot 5 - \dfrac{1}{2} \cdot 4 \cdot 3 \\ &= 30 - 6 \\ &= 24. \end{align*}$$

Thus, B is the correct answer.