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A landscape architect planned a flower garden in the shape of a parallelogram. If the base and height are multiplied by \( \frac{1}{2} \) to create a new parallelogram, what is the new area? Round to the nearest unit, if necessary.

Ask by Hart Joseph. in the United States
Jan 23,2025

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The new area is one fourth of the original area.

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Beyond the Answer

The area of a parallelogram is calculated using the formula: Area = base × height. If the base and height are both multiplied by \( \frac{1}{2} \), the new area can be determined by plugging these values into the formula. Let's denote the original base as \( b \) and the original height as \( h \). The original area is \( A = b \times h \). After scaling down, the new base becomes \( \frac{b}{2} \) and the new height becomes \( \frac{h}{2} \). Thus, the new area \( A' \) is: \[ A' = \left(\frac{b}{2}\right) \times \left(\frac{h}{2}\right) = \frac{1}{4} (b \times h) \] So, the new area is \( \frac{1}{4} \) of the original area. If you round it to the nearest unit and provided the original area, you'd get the exact new area!

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