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Concept 3 of 9

Embedded Figures: Hidden Shapes

1

Today's big idea

A shape counts as embedded only when it fits straight on, at the same size and angle.

Turn it or stretch it to make it fit and it was never really embedded.

2

How it works

👀 What's going on?

A puzzle shows you one busy drawing crammed with lines, then four small shapes underneath it. Only one of them is genuinely sitting inside the drawing, exactly as it is.

💡 Here's the trick

Same size, same angle, no turningFind thisHidden in hereIt fits straight on, so it is embeddedCover the extra lines with a finger and check what is left.

Study the small shape's outline first. Then hunt for those same lines inside the big figure, at the same size and the same angle. If you have to turn it or stretch it to make it fit, it is not embedded.

🪄 How to do it

  1. 1.Count the sides and the corners of the small shape in the picture above.
  2. 2.Trace the big figure slowly, looking for that exact run of lines.
  3. 3.Cover the extra lines with a finger, then check what is left really is the small shape.

✍️ Try it

A five-pointed star is drawn. Is a hidden inside it? Is a square?

Each of the five points is a triangle, so a triangle is embedded. No four square corners appear anywhere in the star, so a square is not.

⚠️ Watch out

A shape can be in the picture and still not count. If the one you are given is bigger, smaller, or tilted compared with what you find, the answer is no. Embedded means it fits straight on, with no turning and no resizing.

🌟 Why this matters

This is the same looking you do when you spot a face in a cloud. It is how you find your own bag in a pile by the door. You hold one outline in your head and scan for it.
Exam tip: Cover the busy parts with your fingers, because the extra lines are drawn in on purpose to hide the shape.

3

Watch me solve one

Quanta solves it

“Watch how I think through one of these — then you try.”

THE PROBLEM

“How many triangles in a 5-pointed star?”

  1. 1

    Identify the points

    A 5-pointed star has 5 points.

  2. 2

    Each point is a triangle

    Count them: 1, 2, 3, 4, 5.

  3. 3

    Answer ✓

    5 triangles

Now you try one — same steps, different story 👇

4

See it in action

⚡ Time to play!

Tap each triangle hidden inside the figure — including the big ones. Find them all.

HIDDEN SHAPES · ROUND 1 OF 3

Figure: a rectangle with both diagonals

triangles found: 0 / 4
5

Quick check

✅ VERIFICATION

A regular hexagon is drawn with all three long diagonals joining opposite corners. Which shape is embedded in it?

⚡ Finish the activity above first to answer.

Keep going!

Up next: Figure Rotation

90° cw: top → right. 180°: flip everything. Pin one corner to verify.

Concept 4 of 9 →