Perimeter, area and volumes: changes in scale

Learning Objectives Define and calculate the linear scale factor between two similar figures or solids. Determine how the perimeter of a 2D figure changes when its linear dimensions are scaled. Calculate the change in area of a 2D figure when its linear dimensions are scaled. Predict the change in volume of a 3D solid when its linear dimensions are scaled. Apply the relationships between linear, area, and volume scale factors to solve real-world problems. Work backward from area or volume scale factors to find the linear scale factor. Have you ever wondered how a model car relates to a real car, or how a small drawing can represent a huge building? 📏 What happens to the measurements when you shrink or enlarge something perfectly? In this lesson, we'll explore how peri...

TermDefinitionExample Scale Factor (Linear)The ratio by which all linear dimensions (like length, width, height, radius, perimeter) of a figure or solid are multiplied to create a similar, larger or smaller figure or solid. It's often denoted by 'k'.If a square with side length 2 cm is enlarged to a square with side length 6 cm, the linear scale factor is $k = \frac{6}{2} = 3$. Similar Figures/SolidsTwo figures or solids are similar if they have the same shape but possibly different sizes. This means their corresponding angles are equal, and their corresponding linear dimensions are proportional (related by a constant scale factor).A small photograph and a larger print of the same photograph are similar figures. A toy car and a real car are similar solids. PerimeterThe tota...

Perimeter Scale Rule If the linear dimensions of a 2D figure are scaled by a linear scale factor $k$, then its perimeter is also scaled by the same linear scale factor $k$. $P_{new} = k \times P_{original}$ This rule applies to any linear measurement, including circumference, height, width, or any distance along the figure. Area Scale Rule If the linear dimensions of a 2D figure are scaled by a linear scale factor $k$, then its area is scaled by the square of the linear scale factor, $k^2$. $A_{new} = k^2 \times A_{original}$ Use this rule to find the area of a scaled figure when you know the original area and the linear scale factor. Volume Scale Rule If the linear dimensions of a 3D solid are scaled by a linear scale factor $k$, then its volume is scaled by the cub...