1. The problem asks for the formula of the area of a semicircle in terms of radians. 2. A semicircle is half of a full circle. 3. The area of a full circle with radius $r$ is given by $$A = \pi r^2$$. 4. Since a semicircle is half of a circle, its area is half of the full circle's area. 5. Therefore, the area of a semicircle is $$A = \frac{1}{2} \pi r^2$$. 6. Note that radians are a measure of angles, and the formula for the area of a semicircle depends on the radius, not directly on the angle in radians. 7. If you are referring to the area of a sector of a circle with angle $\theta$ in radians, the formula is $$A = \frac{1}{2} r^2 \theta$$. 8. For a semicircle, the angle $\theta$ is $\pi$ radians, so substituting gives $$A = \frac{1}{2} r^2 \pi = \frac{1}{2} \pi r^2$$, which matches the semicircle area formula. Final answer: The area of a semicircle is $$A = \frac{1}{2} \pi r^2$$.