A banner which will be hung in the atrium of an office building will be 8 times the size of the model below. The scale model of the banner has a perimeter of 2(2.5) + 2(0.75) = 6.5 feet.
In this section, you will look at ways similarity is used in different careers.
In the design world, a common use of geometry is to use the properties of similar figures to create a scale model of a design for a product that will be later reduced or enlarged to make the real product.
A banner which will be hung in the atrium of an office building will be 8 times the size of the model below. The scale model of the banner has a perimeter of 2(2.5) + 2(0.75) = 6.5 feet.
The real banner, whose dimensions will be 8 times that of the scale model, will have a perimeter that is 8 times the perimeter of the scale model. If the banner is to have special trim around the bordered, how much trim will be needed for the real banner?
6.5 ft × 8 = 52 ft
The designers will need 52 feet, the perimeter of the banner, of trim material for the border of the banner.
Suppose you are a landscaper and your client wants concrete stepping stones made for her back yard. To create the stepping stones you will need to create circular forms which will hold the concrete until it dries.
The client wants three sizes of stones with diameters of 12 inches, 18 inches, and 24 inches. You know that the amount of material you need to make the form for the smallest stone is about 38 inches. How much material do you need to make each of the other stones?
Since all circles are similar figures and the diameter represents both its width and height, the change in diameter will be the same as the change in circumference (Circumference = dπ = d × 3.14). Use what you know about dimensional change to find the amount of form material needed for each stone.
The change (scale factor) from the 12 inch stone to the 18 inch stone is 1.5. Multiply 38 inches (12 × 3.14) by 1.5 for its circumference.
38 × 1.5 = 57 inches
From the 12 inch stone to the 24 inch stone, the increase is a scale factor of 2.
38 × 2 = 76 inches