If the length of the base of a parallelogram is decreased by 30％and the height is increased by 20％ what Is the percent decrease in the area of the parallelogram
original area = base x height = bh
new area = .7b x 1.2h = .84bh
so there is a 16% decrease in the area
To find the percent decrease in the area of a parallelogram when the length of the base is decreased by 30% and the height is increased by 20%, we can follow these steps:
1. Identify the formula for the area of a parallelogram: Area = base × height.
2. Calculate the original area of the parallelogram using the given base and height.
3. Calculate the new base after decreasing it by 30%. This can be done by multiplying the original base by (100% - 30%), or 0.7.
4. Calculate the new height after increasing it by 20%. This can be done by multiplying the original height by (100% + 20%), or 1.2.
5. Calculate the new area of the parallelogram using the new base and height.
6. Calculate the percent decrease in the area by subtracting the new area from the original area, dividing by the original area, and multiplying the result by 100.
Let's apply these steps to a numerical example:
Original base = 10 units
Original height = 8 units
1. Original area = 10 units × 8 units = 80 square units
2. New base = 10 units × 0.7 = 7 units
3. New height = 8 units × 1.2 = 9.6 units
4. New area = 7 units × 9.6 units = 67.2 square units
5. Percent decrease = ((80 - 67.2) / 80) × 100 = 16%
Therefore, the percent decrease in the area of the parallelogram is 16%.