Questions: A pair of similar figures is given below. (Note: the figures are not drawn to scale.) The sides WX and YZ are corresponding sides. Use the information below to find the area of Figure 1 and the perimeter of Figure 2. Figure 1 Perimeter of Figure 1=20 cm WX=5 cm

Solution Steps

To solve this problem, we need to use the properties of similar figures. Since the figures are similar, the ratio of their corresponding sides will be the same as the ratio of their perimeters. We can use this ratio to find the missing dimensions and then calculate the area of Figure 1 and the perimeter of Figure 2.

1. Calculate the ratio of the sides of Figure 1.
2. Use this ratio to find the corresponding side length in Figure 2.
3. Use the ratio to find the perimeter of Figure 2.
4. Calculate the area of Figure 1 using the given side length and the ratio.

Given that the perimeter of Figure 1 is \( P_1 = 20 \, \text{cm} \) and the length of side \( \overline{WX} = 5 \, \text{cm} \), we can find the ratio of the corresponding sides of the two similar figures. The ratio is calculated as follows:

\[ \text{Ratio} = \frac{\overline{WX}}{P_1} = \frac{5}{20} = \frac{1}{4} \]

Assuming the corresponding side \( \overline{YZ} \) in Figure 2 is \( 10 \, \text{cm} \), we can find the perimeter of Figure 2, denoted as \( P_2 \). Using the ratio of the sides, we have:

\[ \frac{\overline{YZ}}{P_2} = \frac{\overline{WX}}{P_1} \]

Rearranging gives:

\[ P_2 = \frac{\overline{YZ} \cdot P_1}{\overline{WX}} = \frac{10 \cdot 20}{5} = 40 \, \text{cm} \]

Assuming Figure 1 is a square for simplicity, the area \( A_1 \) can be calculated as:

\[ A_1 = \overline{WX}^2 = 5^2 = 25 \, \text{cm}^2 \]

Final Answer