1. Let's create a problem involving quadrilaterals. 2. Problem: Given a quadrilateral with vertices at points $A(1,2)$, $B(4,2)$, $C(4,5)$, and $D(1,5)$, find the perimeter and area of the quadrilateral. 3. To find the perimeter, we use the distance formula between consecutive vertices: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 4. Calculate each side length: - $AB = \sqrt{(4-1)^2 + (2-2)^2} = \sqrt{3^2 + 0} = 3$ - $BC = \sqrt{(4-4)^2 + (5-2)^2} = \sqrt{0 + 3^2} = 3$ - $CD = \sqrt{(1-4)^2 + (5-5)^2} = \sqrt{(-3)^2 + 0} = 3$ - $DA = \sqrt{(1-1)^2 + (2-5)^2} = \sqrt{0 + (-3)^2} = 3$ 5. Sum the side lengths to find the perimeter: $$P = AB + BC + CD + DA = 3 + 3 + 3 + 3 = 12$$ 6. Since the quadrilateral is a rectangle (opposite sides equal and all angles 90 degrees), the area is: $$A = \text{length} \times \text{width} = 3 \times 3 = 9$$ 7. Final answer: - Perimeter: $12$ - Area: $9$