Reasoning: How to Solve Embedded Figures - Finding a Given Shape Within a Complex Figure

Introduction "Embedded Figures typically carry 5-10 marks in competitive exams, making it a must-master topic to crack the exam quickly and confidently."

WHAT YOU NEED TO KNOW FIRST To solve Embedded Figures, you need to know:

1. Direction Chart: A simple chart that helps you identify the direction of a shape within a complex figure.
2. BODMAS: A rule to follow when solving mathematical problems, which stands for Brackets, Orders, Division, Multiplication, Addition, and Subtraction.
3. Sitting Arrangement Conventions: Basic rules to follow when solving seating arrangement problems, such as "North" being opposite to "South".

CRYSTAL‑CLEAR METHOD (Step‑by‑Step) To solve Embedded Figures, follow these steps:

1. Identify the given shape: Look for the shape you need to find within the complex figure.
2. Identify the direction: Use the direction chart to determine the direction of the given shape.
3. Look for matching parts: Identify the parts of the complex figure that match the given shape.
4. Use BODMAS to solve mathematical problems: If the problem involves mathematical calculations, use BODMAS to solve them.
5. Use sitting arrangement conventions: If the problem involves seating arrangements, use the conventions to solve it.
6. Combine the information: Combine the information from the previous steps to find the given shape within the complex figure.

WORKED EXAMPLES

Example 1 – Easy Find the shape within the complex figure:

  A B C
D E F
G H I

Given shape: Triangle

Solution:

1. Identify the given shape: Triangle
2. Identify the direction: The direction chart shows that the triangle is pointing upwards.
3. Look for matching parts: The top three letters (A, B, C) form a triangle.
4. Combine the information: The triangle is pointing upwards, and the top three letters form a triangle.

What we learned: To solve Embedded Figures, start by identifying the given shape and its direction.

Example 2 – Medium Find the shape within the complex figure:

  1 2 3
4 5 6
7 8 9

Given shape: Square

Solution:

1. Identify the given shape: Square
2. Identify the direction: The direction chart shows that the square is pointing to the right.
3. Look for matching parts: The middle three numbers (5, 6, 7) form a square.
4. Use BODMAS to solve mathematical problems: None required in this example.
5. Combine the information: The square is pointing to the right, and the middle three numbers form a square.

What we learned: To solve Embedded Figures, use BODMAS to solve mathematical problems if required.

Example 3 – Exam‑Style Find the shape within the complex figure:

  1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16

Given shape: Rectangle

Solution:

1. Identify the given shape: Rectangle
2. Identify the direction: The direction chart shows that the rectangle is pointing to the right.
3. Look for matching parts: The top two rows (1-4, 5-8) form a rectangle.
4. Use sitting arrangement conventions: None required in this example.
5. Combine the information: The rectangle is pointing to the right, and the top two rows form a rectangle.

What we learned: To solve Embedded Figures, use the direction chart and look for matching parts.

Common Mistakes

MISTAKE → WHY IT HAPPENS → CORRECT APPROACH

1. Mistake: Not identifying the given shape correctly. WHY IT HAPPENS: Lack of attention to detail. CORRECT APPROACH: Take your time and carefully examine the complex figure.

2. Mistake: Not using the direction chart. WHY IT HAPPENS: Ignoring the direction chart can lead to incorrect solutions. CORRECT APPROACH: Always use the direction chart to determine the direction of the given shape.

3. Mistake: Not looking for matching parts. WHY IT HAPPENS: Failing to identify matching parts can lead to incorrect solutions. CORRECT APPROACH: Carefully examine the complex figure to identify matching parts.

4. Mistake: Not using BODMAS to solve mathematical problems. WHY IT HAPPENS: Ignoring mathematical problems can lead to incorrect solutions. CORRECT APPROACH: Use BODMAS to solve mathematical problems if required.

5. Mistake: Not combining the information correctly. WHY IT HAPPENS: Failing to combine the information correctly can lead to incorrect solutions. CORRECT APPROACH: Carefully combine the information from the previous steps to find the given shape within the complex figure.

EXAM TRAPS

Trap → How to Spot it → How to Avoid it

1. Trap: The complex figure has multiple shapes that match the given shape. How to Spot it: Look for multiple shapes that match the given shape. How to Avoid it: Carefully examine the complex figure to identify the correct shape.

2. Trap: The complex figure has a shape that is similar to the given shape but not identical. How to Spot it: Look for shapes that are similar but not identical. How to Avoid it: Carefully examine the complex figure to identify the correct shape.

3. Trap: The complex figure has a shape that is rotated or flipped. How to Spot it: Look for shapes that are rotated or flipped. How to Avoid it: Use the direction chart to determine the direction of the given shape.

TIME‑SAVING SHORTCUTS

1. Elimination trick: Eliminate options that are clearly incorrect.
2. Diagram hack: Use a diagram to visualize the complex figure and the given shape.
3. Pattern recognition: Recognize patterns in the complex figure to identify the given shape.

1‑MINUTE RECAP "Alright, let's recap. To solve Embedded Figures, start by identifying the given shape and its direction. Look for matching parts and use BODMAS to solve mathematical problems if required. Combine the information carefully to find the given shape within the complex figure. Remember to avoid common mistakes and exam traps. Use time-saving shortcuts like elimination tricks, diagram hacks, and pattern recognition to save time. You got this! Good luck on your exam."