Question

a deli owner uses 215 square centimeters of plastic wrap to cover a wedge of cheese. how many square centimeters of plastic wrap would she need to cover a wedge of cheese with a similar shape that is smaller by a scale factor of \\(\frac{1}{2}\\)? round to the nearest tenth.

Explanation:

Step1: Recall the scale factor for area

When two similar figures have a scale factor of \( k \), the ratio of their areas is \( k^2 \). Here, the scale factor \( k=\frac{1}{2} \), so the ratio of the areas is \( (\frac{1}{2})^2=\frac{1}{4} \).

Step2: Calculate the area of the smaller wedge

Let the area of the original wedge be \( A_1 = 215\) square centimeters and the area of the smaller wedge be \( A_2 \). We know that \( \frac{A_2}{A_1}=\frac{1}{4} \), so \( A_2=\frac{A_1}{4} \). Substituting \( A_1 = 215 \), we get \( A_2=\frac{215}{4}=53.75 \). Rounding to the nearest tenth, we check the hundredth place (5), so we round up the tenth place. \( 53.75\approx53.8 \).

Answer:

\( 53.8 \) square centimeters