(5) The figures below are similar. If you know the area of the 2nd figure(on right), wh the 1st figure(on left)? 20 cm 15 cm 0% A=240 cm² A. Area = 180 cm² B. Area = 135 cm² C. Area = 105 cm² . Area = 130 cm²
(5) The figures below are similar. If you know the area of the 2nd figure(on right), wh the 1st figure(on left)? 20 cm 15 cm 0% A=240 cm² A. Area = 180 cm² B. Area = 135 cm² C. Area = 105 cm² . Area = 130 cm²
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter63: Volumes Of Pyramids And Cones
Section: Chapter Questions
Problem 34A
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Help on #5
![**Similar Figures and Area Calculation**
**Problem:**
The figures below are similar. If you know the area of the 2nd figure (on the right), what is the area of the 1st figure (on the left)?
**Figures:**
1. **First Figure (on the left):**
- Dimensions: 15 cm (one side)
- Shape: Parallelogram (Approximate)
2. **Second Figure (on the right):**
- Dimensions: 20 cm (one side)
- Area: 240 cm²
- Shape: Parallelogram (Approximate)
**Options:**
A. Area = 180 cm²
B. Area = 135 cm²
C. Area = 105 cm²
D. Area = 130 cm² *(Marked Incorrect)*
**Explanation:**
To solve this problem, you need to use the property of similar figures. Since the figures are similar, the ratio of their corresponding linear dimensions is equal, and the ratio of their areas is the square of the ratio of their corresponding linear dimensions.
Given:
- Side of the first figure = 15 cm
- Side of the second figure = 20 cm
- Area of the second figure = 240 cm²
The ratio of the sides:
\[
\text{Ratio} = \frac{15 \, \text{cm}}{20 \, \text{cm}} = \frac{3}{4}
\]
Now, the ratio of the areas of similar figures is the square of the ratio of their sides:
\[
\left(\frac{3}{4}\right)^2 = \frac{9}{16}
\]
Let \(A_1\) be the area of the first figure. Then:
\[
\frac{A_1}{240 \, \text{cm}^2} = \frac{9}{16}
\]
\[
A_1 = 240 \, \text{cm}^2 \times \frac{9}{16} = 135 \, \text{cm}^2
\]
Therefore, the correct answer is:
**B. Area = 135 cm²**
**Conclusion:**
Through the application of properties of similar figures and proportional reasoning, the area of the first figure is determined to be **135 cm²**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4904ad93-6dcc-43fa-9122-8f69394907f2%2Fc141882f-cad6-48bf-b8a1-3f6246281363%2Fdjzhcil_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Similar Figures and Area Calculation**
**Problem:**
The figures below are similar. If you know the area of the 2nd figure (on the right), what is the area of the 1st figure (on the left)?
**Figures:**
1. **First Figure (on the left):**
- Dimensions: 15 cm (one side)
- Shape: Parallelogram (Approximate)
2. **Second Figure (on the right):**
- Dimensions: 20 cm (one side)
- Area: 240 cm²
- Shape: Parallelogram (Approximate)
**Options:**
A. Area = 180 cm²
B. Area = 135 cm²
C. Area = 105 cm²
D. Area = 130 cm² *(Marked Incorrect)*
**Explanation:**
To solve this problem, you need to use the property of similar figures. Since the figures are similar, the ratio of their corresponding linear dimensions is equal, and the ratio of their areas is the square of the ratio of their corresponding linear dimensions.
Given:
- Side of the first figure = 15 cm
- Side of the second figure = 20 cm
- Area of the second figure = 240 cm²
The ratio of the sides:
\[
\text{Ratio} = \frac{15 \, \text{cm}}{20 \, \text{cm}} = \frac{3}{4}
\]
Now, the ratio of the areas of similar figures is the square of the ratio of their sides:
\[
\left(\frac{3}{4}\right)^2 = \frac{9}{16}
\]
Let \(A_1\) be the area of the first figure. Then:
\[
\frac{A_1}{240 \, \text{cm}^2} = \frac{9}{16}
\]
\[
A_1 = 240 \, \text{cm}^2 \times \frac{9}{16} = 135 \, \text{cm}^2
\]
Therefore, the correct answer is:
**B. Area = 135 cm²**
**Conclusion:**
Through the application of properties of similar figures and proportional reasoning, the area of the first figure is determined to be **135 cm²**.
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