This page covers Agniveer Army CEE Embedded Figures with complete concept notes, 6 graded practice MCQs, key points and exam-specific tips. Free to study.
Core ConceptRead this first — the foundation of the topic
Let's work through an example
Simple Figure: A right triangle with one horizontal line and one vertical line forming a 90-degree angle
Complex Figure Options
1
Identify the key features of the simple figure - right angle, horizontal base, vertical height.
2
Look for the same right angle pattern in each complex figure. Eliminate figures that don't have this exact angle combination.
3
Trace the complete triangle shape within the remaining options. Check if all three sides can be found without breaks or distortions.
4
Verify that the proportions match the original figure. In this case, the correct answer would be the complex figure where you can trace the complete right triangle maintaining its exact shape and proportional relationships. Another effective trick is the 'Elimination Method' - quickly eliminate options that clearly don't contain enough lines or shapes to form the required figure. If the simple figure has 5 distinct line segments, the complex figure must have at least 5 line segments in the correct arrangement.
Exam TrapsCommon mistakes students make — avoid these
include accepting distorted versions of the target figure or missing rotated orientations. Students often get confused when the embedded figure appears upside down or sideways. Remember, rotation is allowed but shape distortion is not.
Practice identifying figures in different orientations to build this skill. The key to mastering embedded figures is systematic scanning and pattern recognition rather than random searching.
Key Points to Remember
Embedded figure maintains exact shape and size but can be rotated or flipped
Simple figure cannot be stretched, distorted, or have proportions changed
Use Corner Method - identify unique angles and corners first for quick elimination
Systematic scanning beats random searching every time
Complex figure must contain at least the same number of line segments as simple figure
Rotation in any direction (90°, 180°, 270°) is perfectly acceptable
A large square is divided into 16 equal smaller squares arranged in a 4×4 grid. How many times does the basic square shape appear as an embedded figure when you count all possible squares of any size that can be formed within this grid?
Practice 2easy
A rectangle is divided into 12 equal smaller rectangles arranged in a 3×4 grid (3 rows and 4 columns). Counting all possible rectangles of any size that can be formed by combining adjacent cells, how many embedded rectangles exist in total?
Practice 3medium
A square of side 8 cm contains a triangle with vertices at three corners of the square. How many complete smaller squares of side 2 cm can be embedded within this triangle without overlapping?
Practice 4medium
A rectangle measuring 12 cm × 6 cm is divided into 12 identical smaller rectangles. If a hexagon is embedded within this grid such that it covers exactly 5 of these smaller rectangles, what is the maximum number of smaller rectangles that can be completely embedded within the hexagon?
Practice 5medium
In a circle of radius 10 cm, a regular pentagon is inscribed. How many non-overlapping circles of radius 2 cm can be embedded entirely within this pentagon?
Practice 6hard
A complex figure consists of a large square with side length 12 cm. Inside it, a triangle with base 8 cm and height 6 cm is embedded. Additionally, a circle with radius 2 cm is embedded within the triangle. If you need to identify which smaller geometric shape is completely embedded (hidden) within the larger composite figure, which of the following statements is correct?
60-Second Revision — Embedded Figures
Remember: Shape and proportions must remain exactly the same
Technique: Use Corner Method to identify unique angles first
Strategy: Eliminate options with insufficient line segments immediately
Alert: Check all four orientations (0°, 90°, 180°, 270°) systematically
Trap: Don't accept distorted or stretched versions of the target figure
Time Management: Maximum 1.5 minutes per question, move on if stuck
Final Check: Trace the complete figure boundary to confirm the answer