jmc

The area of the shaded region is equal to the area of the quarter circle with the area of the rectangle taken away. The area of the rectangle is $4\cdot 3=12$, so we just need the quarter circle. Applying the Pythagorean Theorem to $△ADC$, we have $$(AC{)}^2=4^2+3^2\Rightarrow AC=5$$ Since $ABCD$ is a rectangle, $$BD=AC=5$$ Clearly $BD$ is a radius of the circle, so the area of the whole circle is $5^2\pi =25\pi$ and the area of the quarter circle is $\frac{25\pi }{4}$. Finally, the shaded region is $$\frac{25\pi }{4}-12\approx 7.6$$ so the answer is $\boxed{7\text{ and }8}$