If you were given the area of a figure and told that all the dimensions of the figure would be cut in half, how could you find the area of the new similar figure?
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If you were given the area of a figure and told that all the dimensions of the figure would be cut in half, how could you find the area of the new similar figure?
Multiply the area of the original figure by .
Divide the area of the original figure by .
Multiply the area of the original figure by 4.
Divide the area of the original figure by 4.
Multiply the area of the original figure by 1/2
To find the area of the new similar figure when all dimensions are cut in half, you would need to follow these steps:
1. Start by determining the original area of the figure.
2. Raise the original area to the power of 2/3 (2/3 because the dimensions are being cut in half).
3. Multiply the result by 1/4 (1/4 because 2/3 × 1/2 = 2/6 = 1/3 and 1/3 × 1/4 = 1/12).
4. The final result will be the area of the new similar figure.
Let me explain in more detail:
1. Determine the original area of the figure:
- If the figure is a square or rectangle, you can find the area by multiplying the length and width.
- If it's a circle, use the formula A = πr², where A is the area and r is the radius.
- If it's a triangle, use the formula A = (1/2)bh, where A is the area, b is the base, and h is the height.
- For other shapes, use their respective area formulas.
2. Raise the original area to the power of 2/3:
- Let's assume the original area is 'A'. Calculate A^(2/3), where ^(2/3) represents raising to the power of 2/3. This step accounts for the reduction of each dimension by half.
3. Multiply the result by 1/4:
- Take the result from step 2 and multiply it by 1/4. This step accounts for the reduction in area due to both dimensions being cut in half.
4. The final result will be the area of the new similar figure after the dimensions are halved.
It's important to note that these steps assume the shape remains the same, and the dimensions are uniformly reduced by half.