A scale factor affects the area of a shape by changing its dimensions. Specifically, you multiply the original area by the scale factor squared (scale factor2) to find the new area.
Here's a breakdown:
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Scale Factor and Linear Dimensions: When you apply a scale factor to a shape, you're multiplying its length and width (or base and height) by that factor.
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Area Calculation: The area of a two-dimensional shape is calculated by multiplying two dimensions (e.g., length x width for a rectangle).
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Impact on Area: Because you're multiplying two dimensions by the scale factor, the area is multiplied by the scale factor twice. This is equivalent to multiplying the area by the square of the scale factor.
Example:
Imagine a rectangle with a length of 3 units and a width of 4 units.
- Original Area = length x width = 3 x 4 = 12 square units
Now, let's apply a scale factor of 2.
- New Length = 3 x 2 = 6 units
- New Width = 4 x 2 = 8 units
- New Area = 6 x 8 = 48 square units
Notice that the new area (48) is 4 times the original area (12). This is because the scale factor (2) was squared (22 = 4). So, 12 * 4 = 48.
Formula:
New Area = Original Area x (Scale Factor)2
In summary: When dealing with area and scale factors, remember to square the scale factor. This gives you the factor by which the original area is multiplied to get the scaled area.
