Have you ever wondered how a map will tell you the exact location of a place? Or do you know how a builder takes the blueprint of a building and turns it into a reality? All of these things are possible with the help of the mathematical concept of the scale factor. So, without further delay, let’s learn how to find scale factor to make your drawings and designs perfectly done!
What is Scale Factor, & How Does It Work?
The scale factor is known as a parameter that is used to reduce or enlarge the sizes of figures in two-dimensional and three-dimensional geometry. It can be used to make similar shapes but with different measurements.
A scale factor is a ratio between the corresponding measurements of an object and a representation of that object. If the scale factor is a whole number, the new object will be larger, and if the scale factor is a fraction, the new object will be smaller.
You can easily find the scale factor by understanding this example: if you have a square of sides 4 cm, you can make a bigger one by multiplying each side by a number, say 2. The new figure you get will be a copy of the original figure, but all its dimensions will be twice the original square. In this example, the 2 will be called the scale factor.
Moreover, if the scale factor is a fraction, the figure will be smaller. This is called reduction. Therefore, if you have a square of sides 4 cm, you can make a smaller one by dividing each side by a fraction, like ½. The new square you get will be a copy of the original square, but all its dimensions will be half of the original figure.
Note: The scale factor only changes the side lengths or dimensions of shapes; however, it does not change the angle measures.
How to Find Scale Factor of Similar Figures?
The scale factor can be determined when the new dimensions and the original dimensions are mentioned. However, two types of scale factors need to be understood before using it. When the size of a figure increases, we say it has been scaled up; when it decreases, we say it has been scaled down.
1. Scale Up
In scale-up, the smaller figure is enlarged to a bigger one. To find the scale factor, use the formula:
Scale factor = larger figure dimensions / Smaller figure dimensions
The scale factor for increasing is always greater than 1. For instance, if the dimension of the larger shape is 18 and that of the smaller one is 6, let us put the values in this formula, which makes it:
Scale Factor = 18/6
Scale factor = 3
That’s how we can see that the scale factor of scaling up is greater than 1.
2. Scale Down
In scale down, the larger figure is reduced to a smaller one. You can find the scale factor by using the formula:
Scale factor = Smaller figure dimensions / Larger figure dimensions
The scale factor for decreasing is always less than 1. For instance, if the dimension of the smaller shape is 6 and that of the larger one is 24, let us put the values in this formula, which makes it:
Scale factor = 18 / 6
Scale factor = 1/3
That’s how we see that the scale factor of scaling down is less than 1.
5 Practical Uses of Scale Factors in Everyday Life
Some of the most common uses of scale factor are:
- Architectural Design: Architects find the scale factor to make models and drawings of buildings. A model will be built at a downscale, allowing designers to represent an original-sized structure in a more convenient and all-inclusive way.
- Map Making: Cartographers apply scale factors in map making. Maps are often smaller depictions of bigger geographical areas, and the scale factor helps maintain exactness when relocating real-world distances to the map.
- 3D Printing: In the era of 3D printing, scale factors are essential for adjusting the size of a visual model before printing. It ensures that the actual object matches the calculated dimensions in the visual design.
- Engineering Prototypes: Engineers find the scale factor when proceeding with prototypes. By making scaled-down models, they can estimate the structural functionality, integrity, and elegance of a product before completing a full-scale production.
- Geometry in Art: Fine artists use scale factors to construct proportional and aesthetic artwork. Whether making paintings or sculptures, artists may apply scale factors to ensure exact and pleasant visual representations.
FAQs
What is the scale factor?
A scale factor is defined as multiplying each dimension of a shape by the same value.
What is the formula for the scale factor of enlarged objects?
You can find the scale factor of the enlargement figure by using this formula:
Scale Factor = Larger object dimensions / Smaller object dimensions.
How to find scale factor of a rectangle?
To find the simple scale factor of two similar rectangles, we divide the length of one side by the size of the corresponding side in the other rectangle.
How do I find the scale factor of a dilation?
First, find the center point of dilation and measure the distance between it and other points on the preimage as well as on the image. We get the scale factor of a dilation from the ratio of these distances.
Final Thoughts
A scale factor is a parameter to enlarge or reduce the figures in geometry. In this article, we have covered everything regarding how to find scale factor of two similar figures. Hope this article will be helpful for you!
