Explain the importance of using the square of the scale factor to calculate the area of a dilated figure

In mathematics and geometry, a dilation is an enlargement in size or a reduction in size of a mathematical object. We perform a dilation of a square by placing the shape on a coordinate plane and multiplying each of the coordinates of the vertices of the square by the same number, called the scale factor. This can also be achieved by multiplying the lengths of each of the sides of a square by the scale factor.

When we dilate a square by a scale factor of k, its sides increase by a factor of k, its area by [tex]k^{2}[/tex], and its volume by [tex]k^{3}[/tex].

So, this is the importance of using the square of the scale factor to calculate the area of a dilated figure.

What is Square?

Square, in geometry, a plane figure with four equal sides and four right (90°) angles. A square is a special kind of rectangle (an equilateral one) and a special kind of parallelogram (an equilateral and equiangular one).

What is scale factor?

The scale factor is a measure for similar figures, who look the same but have different scales or measures. Suppose, two circle looks similar but they could have varying radii. The scale factor states the scale by which a figure is bigger or smaller than the original figure.

What is dilation?

In mathematics and geometry, a dilation is an enlargement in size or a reduction in size of a mathematical object. We perform a dilation of a shape by placing the shape on a coordinate plane and multiplying each of the coordinates of the vertices of the shape by the same number, called the scale factor.

According to question, we have to explain the importance of using the square of the scale factor to calculate the area of a dilated figure.

When we dilate a square by a scale factor of k, its sides increase by a factor of k, its area by [tex]k^{2}[/tex], and its volume by [tex]k^{3}[/tex].

In mathematics and geometry, a dilation is an enlargement in size or a reduction in size of a mathematical object.

We perform a dilation of a square by placing the shape on a coordinate plane and multiplying each of the coordinates of the vertices of the square by the same number, called the scale factor.

This can also be achieved by multiplying the lengths of each of the sides of a square by the scale factor.

Hence, these are the importance of using the square of the scale factor to calculate the area of a dilated figure.

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