Question

1. a scale drawing of an office space uses a scale of 1 in.: 6 yd. the scale drawing has an area of 6 square inches. what is the area of the actual office space?

Explanation:

Step1: Find the scale - factor for area

The linear scale is 1 in. : 6 yd. For area, the scale - factor is the square of the linear scale - factor. The linear scale factor $k = 6$ (since 1 in on the drawing represents 6 yd in real - life), and the area scale factor $k^2=6^2 = 36$. This means that 1 square inch on the drawing represents $36$ square yards in real - life.

Step2: Calculate the actual area

If the area of the scale drawing is $A_{drawing}=6$ square inches, and the area scale factor is 36, then the actual area $A_{actual}$ is given by the formula $A_{actual}=A_{drawing}\times k^2$. Substitute $A_{drawing} = 6$ and $k^2=36$ into the formula: $A_{actual}=6\times36=216$ square yards.

Answer:

216 yd²