- 14. What is the area of this trapezoid? 7m A. 21 m² B. 27 m² C. 26 m² D. 29 m² 5m 4m A= A 12 2 (

Elementary Geometry For College Students, 7e
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ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
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#14
### Trapezoid Area and Circle Similarity Ratio Calculations

#### Problem 14:
**Question:** What is the area of this trapezoid?

There is a diagram of a trapezoid with the following dimensions:
- One base is 7 meters
- The other base is 4 meters
- The height is 5 meters

To calculate the area of the trapezoid, use the formula:
\[ A = \frac{1}{2} \times (a + b) \times h \]
\[ A = \frac{1}{2} \times (7 + 4) \times 5 \]
\[ A = \frac{1}{2} \times 11 \times 5 \]
\[ A = \frac{55}{2} \]
\[ A = 27.5 \, m^2 \]

However, the options given are:
A. 21 m²
B. 27 m²
C. 26 m²
D. 29 m²

The correct choice is the closest to our calculated value:
- **Answer: B. 27 m²**

#### Problem 15:
**Question:** What is the area of a trapezoid with bases 8 and 18.5 inches, legs of 10 and 6.5 inches, and height of 6 inches?

To calculate the area, use the same formula for the area of a trapezoid:
\[ A = \frac{1}{2} \times (a + b) \times h \]
\[ A = \frac{1}{2} \times (8 + 18.5) \times 6 \]
\[ A = \frac{1}{2} \times 26.5 \times 6 \]
\[ A = \frac{1}{2} \times 159 \]
\[ A = 79.5 \, in^2 \]

The options given are:
A. 75 in²
B. 43 in²
C. 79.5 in²
D. 159 in²

- **Answer: C. 79.5 in²**

#### Problem 16:
**Question:** Find the similarity ratio of two circles with areas \(32\pi \, cm^2 \) and \(98\pi \, cm^2\).

The ratio of the areas of circles is equal to the square of the
Transcribed Image Text:### Trapezoid Area and Circle Similarity Ratio Calculations #### Problem 14: **Question:** What is the area of this trapezoid? There is a diagram of a trapezoid with the following dimensions: - One base is 7 meters - The other base is 4 meters - The height is 5 meters To calculate the area of the trapezoid, use the formula: \[ A = \frac{1}{2} \times (a + b) \times h \] \[ A = \frac{1}{2} \times (7 + 4) \times 5 \] \[ A = \frac{1}{2} \times 11 \times 5 \] \[ A = \frac{55}{2} \] \[ A = 27.5 \, m^2 \] However, the options given are: A. 21 m² B. 27 m² C. 26 m² D. 29 m² The correct choice is the closest to our calculated value: - **Answer: B. 27 m²** #### Problem 15: **Question:** What is the area of a trapezoid with bases 8 and 18.5 inches, legs of 10 and 6.5 inches, and height of 6 inches? To calculate the area, use the same formula for the area of a trapezoid: \[ A = \frac{1}{2} \times (a + b) \times h \] \[ A = \frac{1}{2} \times (8 + 18.5) \times 6 \] \[ A = \frac{1}{2} \times 26.5 \times 6 \] \[ A = \frac{1}{2} \times 159 \] \[ A = 79.5 \, in^2 \] The options given are: A. 75 in² B. 43 in² C. 79.5 in² D. 159 in² - **Answer: C. 79.5 in²** #### Problem 16: **Question:** Find the similarity ratio of two circles with areas \(32\pi \, cm^2 \) and \(98\pi \, cm^2\). The ratio of the areas of circles is equal to the square of the
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