Scale drawings

Learning Objectives Interpret a scale and calculate its unitless scale factor. Calculate the actual dimensions and perimeter of an object from a scale drawing. Calculate the actual area of an object from a scale drawing using the area scale factor. Differentiate between the linear scale factor (for perimeter) and the area scale factor. Determine the scale of a drawing given the actual and drawn areas. Apply the principles of scale drawings to solve multi-step, real-world problems involving geometric shapes. How can an architect fit an entire sports stadium onto a single blueprint, and how do they know the real amount of turf needed for the field? 🏟️ This tutorial revisits the fundamentals of scale drawings, a key application of geometric similarity. We will focus on the cri...

TermDefinitionExample Scale DrawingA proportional two-dimensional drawing of an object that is either a reduction or an enlargement of the actual object. It maintains the same shape but has a different size.A floor plan of a house is a scale drawing where 1 cm on the drawing might represent 2 meters in the actual house. ScaleThe ratio that compares a length in the drawing to the corresponding length in the actual object. It can be expressed in words (1 cm to 10 km), as a ratio (1:100), or as a fraction (1/100).A map scale of 1:50,000 means 1 unit of distance on the map represents 50,000 of the same units in reality. Scale Factor (k)A unitless number representing the constant ratio of any length in the scale drawing to its corresponding length on the actual object. To find it, both lengths...

Linear Scale Factor (k) k = \frac{\text{Drawing Length}}{\text{Actual Length}} Use this to find the unitless scale factor. Ensure both lengths are in the same units before calculating. This 'k' is used for finding perimeters and individual side lengths. Perimeter Relationship \text{Perimeter}_{\text{actual}} = \frac{\text{Perimeter}_{\text{drawing}}}{k} The actual perimeter is found by dividing the drawing's perimeter by the scale factor k (or multiplying by 1/k). The ratio of perimeters is the same as the ratio of side lengths. Area Relationship \text{Area}_{\text{actual}} = \frac{\text{Area}_{\text{drawing}}}{k^2} The actual area is found by dividing the drawing's area by the square of the scale factor, k². This is because area is a two-dimensio...