Subjects geometry

Parallelogram Area 1B0378

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1. **State the problem:** We need to find the correct base and height measurements of the parallelogram with vertices at $(-5, -4)$, $(-2, 3)$, $(7, 3)$, and $(4, -4)$ and calculate its area. 2. **Identify the base:** The base is the length of the segment between $(-5, -4)$ and $(4, -4)$. Calculate the distance: $$\text{base} = |4 - (-5)| = |4 + 5| = 9$$ So, the base is 9 units. 3. **Identify the height:** The height is the perpendicular distance between the base line $y = -4$ and the opposite side, which lies on the line $y = 3$. Calculate the height: $$\text{height} = |3 - (-4)| = |3 + 4| = 7$$ So, the height is 7 units. 4. **Calculate the area:** The area of a parallelogram is given by: $$\text{Area} = \text{base} \times \text{height}$$ Substitute the values: $$\text{Area} = 9 \times 7 = 63$$ 5. **Conclusion:** The correct statement is: "The base is 9 and the height is 7, so the area is 9(7) = 63 square units."