In this section, you will look at how the dimensional changes affect the area of a figure.

In the design world, a common use of geometry is to use the properties of similar figures to create aInteractive popup. Assistance may be required. scale model A scale model will have the same shape as the final product but it might be a different size. of a design for a product that will be later reduced or enlarged to make the real product.

Example

A banner will be hung in the atrium of an office building 8 times the size of its scale model below.

Area = (2.5)(0.75) = 1.875 square feet.

The real banner will have both the length and width of the banner increased by a factor of 8. Therefore, the area of the banner will be 8 × 8 or 64 times the area of the model. How much fabric will be needed to make the banner for the atrium?

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Check Your Answer

1.875 ft × 64 = 120 ft². The designers will need 120 square feet of fabric to make the banner.

How much more fabric will be needed to make the banner than was used for the model?

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Check Your Answer

120 ft² − 1.875 ft² =118.125 ft². The designers will need 118.125 square feet more fabric for the banner than the scale model.