Step 1 :Draw a polar coordinate system, which consists of a series of concentric circles (representing different radii) and rays emanating from the origin (representing different angles).
Step 2 :Draw two circles with radii 1 and 2 respectively. This is because the condition 1 ≤ r ≤ 2 means that the rectangle extends from the circle of radius 1 to the circle of radius 2.
Step 3 :Draw two rays at angles of π/4 radians (45 degrees) and 5π/4 radians (225 degrees) counterclockwise from the positive x-axis. This is because the condition π/4 ≤ θ ≤ 5π/4 means that the rectangle extends from the ray at an angle of π/4 radians to the ray at an angle of 5π/4 radians.
Step 4 :Shade the region defined by these four boundaries (the two circles and the two rays). This shaded region is the polar rectangle.