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?
h = X, b = 6x.
Ao = bh = 6x * x = 6x^2.
An = (6x/2) * x = = 3x^2.
An/Ao = 3x^2/6x^2 = 0.50 = 50%.
To find the percentage of the original area when the base of a parallelogram is cut in half, we need to determine the relationship between the original area and the new area.
Let's assume the original base of the parallelogram is "b" and the height is "h." According to the given information, the base is 6 times the height, so we can write this as:
b = 6h
The formula for calculating the area of a parallelogram is:
A = base x height
Therefore, the original area (A₁) can be expressed as:
A₁ = (6h) x h
A₁ = 6h²
Now, let's calculate the new area (A₂) when the base is cut in half. The new base would be b/2 and the height remains the same:
A₂ = (b/2) x h
To determine the percentage of the original area, we divide the new area by the original area and multiply by 100:
Percentage = (A₂ / A₁) x 100
Percentage = [(b/2) x h] / (6h²) x 100
Percentage = (b x h) / (12h²) x 100
Percentage = (1/12) x 100
Percentage = 8.33%
Therefore, when the base of the parallelogram is cut in half, the new area is approximately 8.33% of the original area.