Question

what is the area of the real object that the scale drawing models?
scale factor: 1:7
area =
2 square cm
scale drawing
real object
a. 98 square cm
b. 2 square cm
c. 196 square cm
d. 14 square cm

Explanation:

Step1: Recall the scale - area relationship

If the scale factor of lengths is \(k\), the scale factor of areas is \(k^{2}\). Here, the scale factor of lengths \(k = 7\) (since the scale is \(1:7\), meaning the real - object length is 7 times the scale - drawing length).

Step2: Calculate the area of the real object

Let \(A_{s}\) be the area of the scale drawing (\(A_{s}=2\space cm^{2}\)) and \(A_{r}\) be the area of the real object. The formula for the relationship between the areas of similar figures is \(A_{r}=A_{s}\times k^{2}\). Substitute \(A_{s} = 2\) and \(k = 7\) into the formula: \(A_{r}=2\times7^{2}\).

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Answer:

A. 98 square cm