Final answer:
Scale factor is the ratio of the dimensions of a scale drawing or model to the actual object. To find actual dimensions or areas, you multiply the dimensions of the drawing by the scale factor. Examples include converting the longest side of a triangular flower bed in a scale drawing to its actual size or finding the model size of a boat.
Step-by-step explanation:
The question relates to the use of scale factors in creating scale drawings or models. A scale factor is the ratio of the dimensions of the drawing or model to the dimensions of the actual object. For instance, if the scale factor for a drawing is 1/200, this means that each unit of measurement on the drawing is equivalent to 200 units on the actual object. Thus, each dimension of the actual object is 200 times larger than that of the drawing.
To find the actual dimensions given a drawing and a scale factor, you would multiply the dimensions of the drawing by the scale factor. The area of any shape can be found by using the appropriate area formula and substituting the actual dimensions into that formula.
For example, if you know that the scale factor for a drawing is 1/20 and the longest side of a triangular flower bed in the drawing is 5.5 meters, then the actual length of the longest side would be 5.5 meters multiplied by 20, or 110 meters. Similarly, if a boat model is built using a scale factor of 1/36, and the actual length of the boat is 24 feet, then the length of the model would be 24 feet divided by 36, resulting in a model length of 8 inches.