Embedded Figures Notes for SSC Exams

In embedded figures questions, a small figure is given and you have to find the complex figure that contains it, in the same size and the same direction. These embedded figures notes for SSC explain the method, the key rules and the counting facts that help to solve them.

What Is an Embedded Figure?

An embedded figure is a simple figure that is hidden inside a more complex figure. The question figure is shown first, and the answer figures are given as options. You have to select the option in which the question figure is present.

Rules

• The hidden figure must be of the same size and the same direction as the question figure.
• The figure cannot be turned, flipped or made bigger or smaller.
• The hidden figure may share its lines with other lines of the complex figure.
• Extra lines may be present around the hidden figure.

Method

1. Study the question figure and note its main features: the number of sides, the angles and the lines inside.
2. Look at each option and find the same features.
3. Trace the lines of the question figure in the option with a pencil.
4. Eliminate the options that do not have an important line or angle.
5. Confirm the answer by checking size and direction.

Useful Counting Facts

A polygon of n sides is divided into (n − 2) triangles by diagonals from one vertex.

Solved Examples

Example 1. How many triangles are there in a square with both diagonals drawn?
There are 4 small triangles and 4 large triangles made of two small ones. The total is 8.

Example 2. How many triangles are formed in a hexagon by diagonals from one vertex?
(6 − 2) = 4 triangles.

Example 3. How many squares are there in a large square divided into four equal small squares?
There are 4 small squares and 1 large square. The total is 5.

Tips

• Start with the most unusual part of the question figure, such as a sharp angle or a small line.
• Check the options one by one and cross out the wrong ones.
• Do not be confused by extra lines around the hidden figure.
• Practise with real figures drawn on paper.

Quick Tips

• Find the most unusual line or angle of the question figure first.
• Check size and direction at the end.
• Eliminate the wrong options quickly.
• Draw the question figure on a rough sheet and trace it.

Quick Revision Points

• The hidden figure has the same size and direction.
• The figure cannot be rotated or flipped.
• A polygon of n sides makes (n − 2) triangles by diagonals from one vertex.
• A square with both diagonals has 8 triangles.
• Trace the lines to confirm the answer.

Practice Questions With Answers

1. How many triangles are there in a square with one diagonal?
   Answer: 2
2. How many triangles are there in a square with both diagonals drawn?
   Answer: 8
3. How many squares are there in a square divided into four equal small squares?
   Answer: 5
4. How many triangles are formed in a pentagon by diagonals from one vertex?
   Answer: 3
5. How many triangles are formed in a hexagon by diagonals from one vertex?
   Answer: 4
6. How many right-angled triangles are formed in a rectangle with one diagonal?
   Answer: 2
7. How many small triangles are formed in a regular hexagon by three diagonals through the centre?
   Answer: 6
8. How many squares are there when the midpoints of the sides of a square are joined?
   Answer: 2 (the outer square and the inner square)
9. What is the first step in finding an embedded figure?
   Answer: Study the main features of the question figure
10. Can the hidden figure be rotated or made bigger?
    Answer: No. It must have the same size and direction.

How to Practise This Chapter

Practise figure questions daily on paper, because you must see the figures to learn them. Then attempt timed sets from our practice papers and the previous year papers page. See all topics on the Non Verbal Reasoning notes page, and also read the Reasoning notes and Verbal Reasoning notes. Read the previous topic, Paper Folding and Cutting, and the next topic, Cubes and Dice.

Frequently Asked Questions

What are embedded figures?

They are simple figures hidden inside a complex figure.

Can the hidden figure be rotated?

No. It must have the same size and direction as the question figure.

How do I solve embedded figure questions?

Note the main features of the question figure and check them in each option.

How many triangles are there in a square with both diagonals?

There are 8 triangles.

How many triangles can a polygon of n sides make from one vertex?

It makes (n minus 2) triangles.

What should I look for first?

Look for the most unusual part of the question figure, such as a sharp angle.

Can extra lines be present?

Yes. The complex figure has extra lines around the hidden figure.

Is this topic asked in SSC exams?

Yes. Embedded figures are asked in SSC reasoning papers.

How much time should I take for one question?

About 40 seconds.

What are common mistakes?

Choosing a figure that is the right shape but of a different size or direction.

How can I improve my speed?

Draw figures on paper and practise tracing the lines.

How many questions come from this topic in SSC exams?

Usually one question, but the number changes from year to year.