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With similar objects (where one is an exact scale version of the other) then if the linear measurements are in the ratio 2 : 3 then the areas are in the ratio 22 : 32 which equals 4 : 9.
So if the sides of two triangles have a scale factor of 2/3 then the areas have a scale factor of 4/9.
What else can I help you with?
How does the scale factor apply to the area?
The areas are related by the square of the scale factor.
How does the area change when you have a scale factor of 2?
When the scale factor is 2, the area of a shape increases by a factor of the square of the scale factor. Therefore, if the original area is ( A ), the new area becomes ( 2^2 \times A = 4A ). This means the area quadruples when the dimensions of the shape are scaled by a factor of 2.
How can you use scale factor to find a new perimeter and area?
New perimeter = old perimeter*scale factor New area = Old area*scale factor2
How do you determine surface area of similar objects when it has a scale factor of 2?
For areas: Square the Scale Factor.
Can you just multiply the original area by the scale factor and get the new area?
No, you cannot simply multiply the original area by the scale factor to get the new area. Instead, you need to square the scale factor and then multiply it by the original area. This is because area is a two-dimensional measurement, so any change in dimensions must be applied in both directions. For example, if the scale factor is 2, the new area will be 2² = 4 times the original area.
What are the relationship between the area scale factor and the side length scale factor of similar figures?
The area scale factor is the square of the side length scale factor.
What is the relationship between scale factor and area?
The area is directly proportional to the square of the scale factor. If the scale factor is 2, the area is 4-fold If the scale factor is 3, the area is 9-fold If the scale factor is 1000, the area is 1,000,000-fold
How does scale factor relate to area?
If the scale factor is r, then the new area will be the area of the original multiplied by r^2
How does the scale factor apply to the area?
The areas are related by the square of the scale factor.
How does the area change when you have a scale factor of 2?
When the scale factor is 2, the area of a shape increases by a factor of the square of the scale factor. Therefore, if the original area is ( A ), the new area becomes ( 2^2 \times A = 4A ). This means the area quadruples when the dimensions of the shape are scaled by a factor of 2.
How can you use scale factor to find a new perimeter and area?
New perimeter = old perimeter*scale factor New area = Old area*scale factor2
How do you determine surface area of similar objects when it has a scale factor of 2?
For areas: Square the Scale Factor.
Can you just multiply the original area by the scale factor and get the new area?
No, you cannot simply multiply the original area by the scale factor to get the new area. Instead, you need to square the scale factor and then multiply it by the original area. This is because area is a two-dimensional measurement, so any change in dimensions must be applied in both directions. For example, if the scale factor is 2, the new area will be 2² = 4 times the original area.
What do you have to do to the scale factor to get the area ratio?
Square it.
What does the scale factor between two similar figures tell you about the given measurement perimeters?
Perimeter will scale by the same factor. Area of the new figure, however is the original figures area multiplied by the scale factor squared. .
How is the scale factor the same as the ratio of the area?
The scale factor between two similar figures is the ratio of their corresponding linear dimensions (lengths). When calculating the area of similar figures, the area ratio is equal to the square of the scale factor, since area is a two-dimensional measurement. Thus, if the scale factor is ( k ), the ratio of the areas is ( k^2 ). This relationship illustrates that while the scale factor pertains to linear dimensions, the area ratio reflects the effect of that scaling in two dimensions.
What happens to surface area when dimensions are changed by a scale factor?
The area changes by the square of the same factor.
