In these lessons, we will learn the scale factors of similar figures, the ratio of lengths, perimeters, areas and volumes of similar figures; suitable for Grade 7 or Grade 8 Math.
A scale factor is the factor by which all the components of an object are multiplied in order to create a proportional enlargement or reduction.
The following diagram shows an example of scale factor. Scroll down the page for more examples and solutions on how to use scale factors.
How to use scale to determine the dimensions of a proportional model?
Define scale factor.
Scale factor is similar to a unit scale except no units are given. Scale factor is a ratio comparing the scaled measurement to the actual measurement.
How to use scale factor to sketch a proportional scale model?
A brief course in scale factor for similar geometric figures
Scale Factor is defined as the ratio of any two corresponding lengths in two similar geometric figures.
Similar Figures are figures such that:
This video explains how to find the ratio of areas and ratios of perimeters for similar polygons.
Ratio of perimeters = ratio of sides
Ratio of areas = (ratio of sides)2
Scale Factor/Perimeter Ratio/Area Ratio
Given that the polygon in each pair are similar. Find the scale factor, perimeter ratio and area ratio.
Areas and Perimeters of Similar Figures
This video discusses how to find the ratio of the perimeters and the ratio of the areas of similar figures from the scale factor. Also how to use these ratios to find missing perimeters and areas.
If the scale factor of two similar figures is a/b, then
How does scale factor impact side lengths, perimeter, area, and angles?
If the scale factor from A to B is x then
The side lengths of B will be x times larger than A
The perimeter of B will be x times larger than A
The area of B will be x2 times larger than A
A and B will have the same shape and angles.
Scale Factor, Length, Area and Volume for similar shapes
Ratio of lengths = ratio of sides = scale factor
Ratio of surface areas = (ratio of sides)2 = (scale factor)2
Ratio of volume = (ratio of sides)3 = (scale factor)3
Surface Areas And Volumes Of Similar Solids
Similar solids have the same shape, and all their corresponding dimensions are proportional.
If the scale factor of two similar solids is a:b, then
• the ratio of their corresponding areas is a2:b2
• the ratio of their volumes is a3:b3
Similar Figures, Scale Factor, Area & Volume Ratios
3D Figures - Scale Models and Factors
Learn about scaling 3D figures using scale factor
Problem: A 6 cm by 2 cm rectangular prism is built form small rectangular prisms of length 3 cm.
a) What is the scale factor from the smaller to the larger model?
b) Find the width and height of the smaller rectangular prisms.
c) Compare the surface area of the two rectangular prisms.
d) Compare the volume of the two rectangular prisms.
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