1. The problem is to find the area of a semicircle with diameter 7 units. 2. The formula for the area of a semicircle is half the area of a full circle: $$\text{Area} = \frac{1}{2} \pi r^2$$ where $r$ is the radius. 3. The radius $r$ is half the diameter, so $$r = \frac{7}{2}$$. 4. Substitute $r$ into the area formula: $$\text{Area} = \frac{1}{2} \pi \left(\frac{7}{2}\right)^2$$ 5. Simplify the square: $$\left(\frac{7}{2}\right)^2 = \frac{49}{4}$$ 6. Substitute back: $$\text{Area} = \frac{1}{2} \pi \frac{49}{4}$$ 7. Multiply the fractions: $$\text{Area} = \frac{49}{8} \pi$$ 8. Therefore, the area of the semicircle is $$\boxed{\frac{49}{8} \pi}$$ square units. This means the semicircle's area is $\frac{49}{8} \pi$, which is approximately 19.24 when $\pi \approx 3.1416$.