Perimeters in Scale Drawings
Perimeters in scale drawings is a Grade 7 math skill in Big Ideas Math Advanced 2, Chapter 12: Constructions and Scale Drawings. To find the actual perimeter from a scale drawing, convert each dimension using the scale factor and then add all actual side lengths. The ratio of actual perimeter to drawing perimeter equals the scale factor, making it possible to multiply the drawing perimeter directly by the scale factor.
Key Concepts
To find the actual perimeter from a scale drawing: first find each actual dimension using the scale, then add all actual side lengths. The ratio of actual perimeter to drawing perimeter equals the scale factor: $\frac{\text{actual perimeter}}{\text{drawing perimeter}} = \text{scale factor}$.
Common Questions
How do you find the actual perimeter from a scale drawing?
Convert each side length from drawing measurements to actual measurements using the given scale, then add all actual side lengths to find the total perimeter.
What is the relationship between scale factor and perimeter?
The actual perimeter equals the drawing perimeter multiplied by the scale factor. For example, if the drawing perimeter is 8 cm and the scale factor is 5, the actual perimeter is 40 units.
How is perimeter scaling different from area scaling?
Perimeter scales by multiplying by the scale factor directly, while area scales by multiplying by the square of the scale factor. This is why area calculations require more care than perimeter.
What textbook covers perimeters in scale drawings in Grade 7?
Big Ideas Math Advanced 2, Chapter 12: Constructions and Scale Drawings covers how to calculate perimeters using scale drawing proportions.