The base of a parallelogram is 6 times its
height if the base is cut in half,the new area is what percentage of the original area?
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To find the answer, we need to follow these steps:
Step 1: Understand the problem.
Let's assume the height of the parallelogram is h units and the base is b units.
Step 2: Set up the given information.
We know that the base of the parallelogram is 6 times its height, so we can write:
b = 6h
Step 3: Find the area of the original parallelogram.
The area of a parallelogram is given by the formula:
Area = base * height
Substituting the values, we get:
Area = b * h
Step 4: Find the new area when the base is reduced by half.
When the base is cut in half, the new base becomes b/2. So, the new area will be:
New Area = (b/2) * h
Step 5: Calculate the percentage of the original area.
To find the percentage, we compare the new area to the original area. The percentage can be calculated using the formula:
Percentage = (New Area / Original Area) * 100
Let's substitute the values to solve the problem:
Original Area = b * h
New Area = (b/2) * h
Percentage = (New Area / Original Area) * 100
Plugging in the value of b = 6h, we get:
Original Area = (6h) * h = 6h^2
New Area = (6h/2) * h = 3h^2
Substituting these values into the percentage formula, we have:
Percentage = (3h^2 / 6h^2) * 100 = (1/2) * 100 = 50%
Therefore, the new area is 50% of the original area.