Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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### Finding the Areas of Shaded Portions in Quilt Patterns

Below are quilt patterns with their shaded portions. Each side of the squares in these patterns is given as 6 cm. Your task is to calculate the area of the shaded regions.

#### Quilt Patterns:
1. **Card Trick (Pattern a.)**
   - Dimensions: 6 cm x 6 cm
   - Description: The pattern consists of overlapping triangles and shapes creating a card trick visual effect.

2. **Linoleum (Pattern b.)**
   - Dimensions: 6 cm x 6 cm
   - Description: This pattern features alternating colored squares, forming a linoleum-like appearance.

3. **Churn Dash (Pattern c.)**
   - Dimensions: 6 cm x 6 cm
   - Description: This pattern consists of a central square surrounded by rectangular and triangular forms.

4. **Friendship Star (Pattern d.)**
   - Dimensions: 6 cm x 6 cm
   - Description: The pattern shaped like a star inscribed within a square.

#### Problem:
Calculate the area of the shaded portions for each of the quilt patterns (a to d).

- **Figure (a):** 
  - The area of the shaded portion is \( \_\_\_\_ \). (Type an integer or a simplified fraction.)

- **Figure (b):** 
  - The area of the shaded portion is \( \_\_\_\_ \). (Type an integer or a simplified fraction.)

- **Figure (c):** 
  - The area of the shaded portion is \( \_\_\_\_ \). (Type an integer or a simplified fraction.)

- **Figure (d):** 
  - The area of the shaded portion is \( \_\_\_\_ \). (Type an integer or a simplified fraction.)

#### Instructions:
1. Review each quilt pattern carefully.
2. Consider the entire area of the square, which is \( 6 \text{ cm} \times 6 \text{ cm} \).
3. Analyze the shaded areas within the pattern.
4. Calculate the area of the shaded regions and provide your answer in the provided fields.

Happy learning!
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Transcribed Image Text:### Finding the Areas of Shaded Portions in Quilt Patterns Below are quilt patterns with their shaded portions. Each side of the squares in these patterns is given as 6 cm. Your task is to calculate the area of the shaded regions. #### Quilt Patterns: 1. **Card Trick (Pattern a.)** - Dimensions: 6 cm x 6 cm - Description: The pattern consists of overlapping triangles and shapes creating a card trick visual effect. 2. **Linoleum (Pattern b.)** - Dimensions: 6 cm x 6 cm - Description: This pattern features alternating colored squares, forming a linoleum-like appearance. 3. **Churn Dash (Pattern c.)** - Dimensions: 6 cm x 6 cm - Description: This pattern consists of a central square surrounded by rectangular and triangular forms. 4. **Friendship Star (Pattern d.)** - Dimensions: 6 cm x 6 cm - Description: The pattern shaped like a star inscribed within a square. #### Problem: Calculate the area of the shaded portions for each of the quilt patterns (a to d). - **Figure (a):** - The area of the shaded portion is \( \_\_\_\_ \). (Type an integer or a simplified fraction.) - **Figure (b):** - The area of the shaded portion is \( \_\_\_\_ \). (Type an integer or a simplified fraction.) - **Figure (c):** - The area of the shaded portion is \( \_\_\_\_ \). (Type an integer or a simplified fraction.) - **Figure (d):** - The area of the shaded portion is \( \_\_\_\_ \). (Type an integer or a simplified fraction.) #### Instructions: 1. Review each quilt pattern carefully. 2. Consider the entire area of the square, which is \( 6 \text{ cm} \times 6 \text{ cm} \). 3. Analyze the shaded areas within the pattern. 4. Calculate the area of the shaded regions and provide your answer in the provided fields. Happy learning!
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