1. **State the problem:** We need to find the perimeter and area of a parallelogram-shaped cookie cutter with vertices at points $A(3,2)$, $B(4,4)$, $C(6,4)$, and $D(5,2)$ on a coordinate grid where each unit is 1 cm. 2. **Assumptions:** We assume the shape is a parallelogram with vertices given in order $A$, $B$, $C$, $D$. The sides are straight lines between these points. 3. **Find the lengths of the sides to calculate the perimeter:** - Length $AB = \sqrt{(4-3)^2 + (4-2)^2} = \sqrt{1^2 + 2^2} = \sqrt{5}$ cm. - Length $BC = \sqrt{(6-4)^2 + (4-4)^2} = \sqrt{2^2 + 0^2} = 2$ cm. - Length $CD = \sqrt{(5-6)^2 + (2-4)^2} = \sqrt{(-1)^2 + (-2)^2} = \sqrt{5}$ cm. - Length $DA = \sqrt{(3-5)^2 + (2-2)^2} = \sqrt{(-2)^2 + 0^2} = 2$ cm. 4. **Calculate the perimeter:** $$\text{Perimeter} = AB + BC + CD + DA = \sqrt{5} + 2 + \sqrt{5} + 2 = 2\sqrt{5} + 4$$ 5. **Simplify the perimeter:** $$2\sqrt{5} + 4 \approx 2 \times 2.236 + 4 = 4.472 + 4 = 8.472$$ Rounded to the nearest hundredth: $8.47$ cm. 6. **Calculate the area using the vector cross product method:** - Vector $\vec{AB} = (4-3, 4-2) = (1, 2)$ - Vector $\vec{AD} = (5-3, 2-2) = (2, 0)$ Area of parallelogram = magnitude of the cross product of $\vec{AB}$ and $\vec{AD}$: $$|\vec{AB} \times \vec{AD}| = |1 \times 0 - 2 \times 2| = |0 - 4| = 4$$ 7. **Final answers:** - Perimeter $\approx 8.47$ cm - Area $= 4$ cm$^2$ These are the perimeter and area of each cookie made with the parallelogram-shaped cutter.