1. **Stating the problem:** Calculate the perimeter $O$ and area $o$ of the rectangle with vertices $A(2,1)$, $B(-2,1)$, $C(-2,-1)$, and $D(2,-1)$. 2. **Formula for distance between two points:** $$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$$ 3. **Calculate side lengths:** - $d(A,B) = \sqrt{(2 - (-2))^2 + (1 - 1)^2} = \sqrt{(4)^2 + 0^2} = \sqrt{16} = 4$ - $d(B,C) = \sqrt{(-2 - (-2))^2 + (1 - (-1))^2} = \sqrt{0^2 + (2)^2} = \sqrt{4} = 2$ 4. **Calculate perimeter $O$:** $$O = 2a + 2b = 2 \cdot 4 + 2 \cdot 2 = 8 + 4 = 12$$ 5. **Calculate area $o$:** Area of rectangle = length $\times$ width $$o = 4 \times 2 = 8$$ **Final answers:** $$O = 12$$ $$o = 8$$