I'm not math-y enough to even begin to go about proving this, but just based on logic I believe you can just cut the circle in half to give you a semicircle with a diameter of $$1$$ unit, which would have an area of $$\tfrac{1}{8} \pi$$ (a circle with a diameter of $$1$$ has an area of $${\pi \cdot\tfrac{1}{2}}^2 = \tfrac{1}{4}\pi$$).