Question

1. these polygons are scaled copies. determine the perimeter of the larger polygon. show or explain your thinking. unit 3 lesson 1

Explanation:

Step1: Calculate the perimeter of the smaller polygon

The perimeter of a polygon is the sum of its side lengths.
For the smaller polygon, the side lengths are \(7\mathrm{cm}\), \(9\mathrm{cm}\), \(8\mathrm{cm}\), \(11\mathrm{cm}\), and \(6\mathrm{cm}\).

$$P_{\text{small}}=7 + 9+8 + 11+6=41\mathrm{cm}$$

Step2: Find the scale factor

The corresponding side lengths of the two polygons: one side of the smaller polygon is \(9\mathrm{cm}\) and the corresponding side of the larger polygon is \(13.5\mathrm{cm}\).
The scale factor \(k=\frac{13.5}{9}=1.5\)

Step3: Calculate the perimeter of the larger polygon

Since the perimeters of similar polygons are in the same ratio as the scale factor.
If \(P_{\text{small}}\) is the perimeter of the smaller polygon and \(P_{\text{large}}\) is the perimeter of the larger polygon, and \(k\) is the scale factor, then \(P_{\text{large}}=k\times P_{\text{small}}\)

$$P_{\text{large}}=1.5\times41 = 61.5\mathrm{cm}$$

Answer:

The perimeter of the larger polygon is \(61.5\mathrm{cm}\)