Final answer:
To compute the new area of the logo after scaling it down to one fourth of its original dimensions, we square the scale factor (1/4)^2 and multiply it by the original area. The area of the logo for the business cards will be 1/4 square inch.
Step-by-step explanation:
To solve the problem of reducing the dimensions of a company's logo by one fourth to use on business cards, where the area of the original logo is 4 square inches, we need to understand the relationship between the scale factor and the area of similar shapes.
When a two-dimensional figure like a logo is scaled down, the scale factor applies to both dimensions (length and width). If the company wants to reduce the dimensions of their logo to one fourth of the original size, the scale factor is 1/4. This means that each dimension of the logo is multiplied by 1/4. However, since area is two-dimensional, the overall area of the reduced logo will actually be the scale factor squared.
The area of the original logo is 4 square inches. To find the area of the smaller logo, we square the scale factor, which is (1/4) squared, or 1/16, and apply it to the original area:
4 square inches * (1/4)^2 = 4 square inches * 1/16 = 1/4 square inches.
Therefore, the area of the logo that will be used on the business cards is 1/4 square inch.