Question

if this rectangle is enlarged by the scale factor of 1/3, what will be the area of the new shape? 6 cm 9 cm a. 18 cm² b. 6 cm² c. 162 cm² add text in 2013 in the arctic oil company suspended dri british petroleum shell exxon

Explanation:

Step1: Recall area - scale factor relationship

The area of a figure changes by the square of the scale - factor when the figure is scaled.

Step2: Calculate the new area

The original rectangle has length \(l = 9\mathrm{cm}\) and width \(w = 6\mathrm{cm}\), so the original area \(A_1=l\times w=9\times6 = 54\mathrm{cm}^2\). The scale factor \(k = 1/3\). The new area \(A_2=A_1\times k^{2}\). Substituting the values, we have \(A_2 = 54\times(\frac{1}{3})^{2}\).

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Answer:

b. \(6\mathrm{cm}^2\)