Answer :
We are going to define the following variables:
A: Area of the original figure.
k: scale factor.
We have that the area of the new figure (reduced or enlarged, depends on the value of k) is:
A '= k ^ 2 * A
Example: rectangle of dimensions (2) * (3) A factor of k = 2 is extended. Find the new area.
The original area is:
A = (2) * (3) = 6
The new area will be:
A '= (2 * 2) * (2 * 3) = 4 * 6 = 24
Or equivalently:
A '= k ^ 2 * A
A '= (2) ^ 2 * (6) = 4 * 6 = 24
A: Area of the original figure.
k: scale factor.
We have that the area of the new figure (reduced or enlarged, depends on the value of k) is:
A '= k ^ 2 * A
Example: rectangle of dimensions (2) * (3) A factor of k = 2 is extended. Find the new area.
The original area is:
A = (2) * (3) = 6
The new area will be:
A '= (2 * 2) * (2 * 3) = 4 * 6 = 24
Or equivalently:
A '= k ^ 2 * A
A '= (2) ^ 2 * (6) = 4 * 6 = 24
When the scale factor and dimensions are given we need to multiply the dimension by the scale factor to get the area of a reduced or enlarged figure.
What is the scale factor?
A scale factor is generally a decimal number(or a ratio) that multiplies or scales a number. For example, If in a map 1 inch is equal to 100 feet in real, then the scale factor can be written as,
[tex]\dfrac{\text{Length on the map}}{\text{Length on the reality}} = \dfrac{1\rm\ in}{100\feet\rm\ feet}[/tex]
When the problem of the reduced or enlarged area occurs, we need to reduce or enlarge each of the dimensions by the scale factor which is given to us in order to get the area of the reduced or the enlarged figure.
Hence, when the scale factor and dimensions are given we need to multiply the dimension by the scale factor to get the area of a reduced or enlarged figure.
Learn more about Scale Factor:
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