### Finding the Areas of Shaded Portions in Quilt PatternsBelow 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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Description: ### Finding the Areas of Shaded Portions in Quilt PatternsBelow 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:

The shaded region consists of four squares of length 2√2 cm. If we look closely we see that in the…

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Find the areas of the shaded portions of the quilt patterns shown below if one side of each square is 6 cm. b. С. d. a. 6 cm { 6 ст 6 cm 6 cm Card trick Linoleum Churn dash Friendship Star a. For figure (a), the area of the shaded portion is (Type an integer or a simplified fraction.) b. For figure (b), the area of the shaded portion is (Type an integer or a simplified fraction.) c. For figure (c), the area of the shaded portion is (Type an integer or a simplified fraction.) d. For figure (d), the area of the shaded portion is (Type an integer or a simplified fraction )

Find the areas of the shaded portions of the quilt patterns shown below if one side of each square is 6 cm. b. С. d. a. 6 cm { 6 ст 6 cm 6 cm Card trick Linoleum Churn dash Friendship Star a. For figure (a), the area of the shaded portion is (Type an integer or a simplified fraction.) b. For figure (b), the area of the shaded portion is (Type an integer or a simplified fraction.) c. For figure (c), the area of the shaded portion is (Type an integer or a simplified fraction.) d. For figure (d), the area of the shaded portion is (Type an integer or a simplified fraction )

Advanced Engineering Mathematics

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ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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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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