Question

shannons tv, figure d, has a height of 22 in. and width of 33 in. shannon drew a scale model of her tv screen, figure e, with a height of 4 in. width of 6 in. use this information to complete problems 1 - 5.

1. what is the scale factor from figure d to figure e?
2. what is the area of shannons tv screen?
3. what is the area of shannons scale model?
4. what is the ratio of the area of figure e to the ratio of the area of figure d?
5. what is the relationship between the scale factor and the ratios of the areas?

Explanation:

Step1: Find scale factor

Scale factor = $\frac{\text{dimension of Figure E}}{\text{dimension of Figure D}}$. Using height: $\frac{4}{22}=\frac{2}{11}$. Using width: $\frac{6}{33}=\frac{2}{11}$.

Step2: Calculate area of Figure D

Area of a rectangle = height × width. So, $A_D = 22\times33 = 726$ in².

Step3: Calculate area of Figure E

Using the same formula, $A_E=4\times6 = 24$ in².

Step4: Find ratio of areas

Ratio = $\frac{A_E}{A_D}=\frac{24}{726}=\frac{4}{121}$.

Step5: Relate scale factor and area ratio

The scale factor is $\frac{2}{11}$, and $(\frac{2}{11})^2=\frac{4}{121}$, which is the ratio of the areas.

Answer:

1. The scale factor is $\frac{2}{11}$.
2. The area of Shannon's TV screen (Figure D) is $726$ in².
3. The area of the scale - model (Figure E) is $24$ in².
4. The ratio of the area of Figure E to Figure D is $\frac{4}{121}$.
5. The ratio of the areas is the square of the scale factor.