2. Given the vertex of a cone is $P$, the radius of the base is 2, and the height is 1. Take a point $Q$ on the base of the cone such that the angle between the line $P Q$ and the base is no greater than $45^{\circ}$. Then the area of the region formed by the points $Q$ that satisfy the condition is $\qquad$.
According to the problem, the locus of point $Q$ that satisfies the condition is the region formed by the annulus with the center at the center of the base of the cone and radii of 1 and 2. Its area is $4 \pi - \pi = 3 \pi$.