LR11 — Embedded Figures and Hidden Figures

🧠 AFCAT Reasoning · LR11 ✈️ AFCAT Level

📌 AFCAT Pattern (LR11): Embedded Figures tests your ability to find a simpler shape hidden within a complex figure. 2–3 questions per paper. The simple shape must appear with the same size and orientation (rotation is possible). Train your eye to separate lines belonging to the target shape from distracting background lines.

1. Core Concept

A simple figure (Question Figure) is shown. Four complex figures (Answer Options) are given. Identify which complex figure contains the question figure embedded within it — same size, possibly different orientation.

Rules of Embedding

The embedded shape must appear at the EXACT SAME SIZE
The shape can be rotated (oriented differently)
The shape can be reflected (flipped) in some questions
ALL lines of the embedded shape must exist in the complex figure
Extra lines in the complex figure are distractors — ignore them

4-Step Method

Step 1: Study the question figure carefully — note exact angles and line lengths
Step 2: In each answer option, trace if the question figure's lines exist
Step 3: Mentally block out distracting lines from the complex figure
Step 4: If all lines of the question figure form a continuous shape in the option, it is correct

📌 AFCAT Tip: The most common error is finding a shape that looks similar but is wrong in proportion. Always count the sides and verify the angles match the original question figure exactly.

2. Counting Embedded Shapes

Some questions ask: How many triangles (or squares) are in this figure? Systematic counting is required.

Worked Example — Count Triangles

A large triangle is divided by 2 lines from apex to base, creating 3 sections.
Count: Small triangles (3: left, middle, right). Medium triangles formed by 2 sections (2: left+middle, middle+right). Full large triangle (1). Total = 3+2+1 = 6 triangles.
Rule: For n lines dividing a triangle: Total triangles = n(n+2)(2n+1)/8 (for standard cases). In practice, count systematically by size.

📝 AFCAT PYQEmbedded Figures — AFCAT Pattern

Q1. A right triangle is the question figure. Which complex figure contains this right triangle? (AFCAT I 2025)
[Options: (a) Square divided diagonally (b) Pentagon (c) Rectangle (d) Irregular hexagon]

(a) Option a — Square divided diagonally
(b) Option b — Pentagon
(c) Option c — Rectangle
(d) Option d — Irregular hexagon

Answer: (a) Square divided diagonally
A square divided by a diagonal creates two right triangles. The question figure (right triangle) is clearly embedded in a square with a diagonal. The diagonal IS the hypotenuse of the right triangle; two sides of the square form the legs. Always: diagonal lines within rectangles/squares create embedded right triangles.

Q2. How many triangles are there in a figure consisting of a large triangle divided by 3 internal lines from each vertex to the midpoint of the opposite side? (AFCAT II 2024)

(a) 6
(b) 8
(c) 12
(d) 10

Answer: (a) 6
When a triangle is divided by medians (lines from vertex to midpoint of opposite side), it creates 6 smaller triangles of equal area. This is a standard result: 3 medians divide any triangle into exactly 6 triangles (all equal in area). Count: 6 small triangles meeting at the centroid.

⚡ Quick Reference — LR11

Embedding Rules

Same size as question figure
Can be rotated or reflected
ALL lines must exist in complex figure
Extra lines = distractors; ignore them

Counting Triangles

Count small, medium, large separately
3 medians → 6 triangles (standard)
n lines parallel → n(n+2)(2n+1)/8
Systematic size-based counting always works

AFCAT Tip

Trace the target shape with fingertip or pen
Mentally block out extra lines
Verify ALL sides — not just the obvious ones
Check proportion: same-size embedding only

📝 AFCAT Mock Tests 🎯 Reasoning Quiz ✈️ Telegram