Spatial Reasoning and Awareness Tests | AssessmentDay - Free Printable

Let's solve this step-by-step.

We are given four individual shapes on the left:

1. A right triangle
2. A regular hexagon
3. A rectangle (long and narrow)
4. A square

We are to determine which of the three figures (A, B, or C) can be made using all these shapes exactly once, without resizing them — only rotating or moving them.

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Step 1: Analyze the original shapes

- Triangle: Right-angled triangle
- Hexagon: Regular hexagon (6 equal sides)
- Rectangle: Long rectangle (looks like twice as long as it is wide)
- Square: Equal sides

All shapes must be used once, and no resizing is allowed.

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Step 2: Check each option

#### Option A:

Let’s examine Figure A:
- There is a triangle in the top-left corner.
- A hexagon placed next to it.
- A square below the triangle.
- A rectangle extending to the right from the square.

Now check if the shapes match:

- The triangle matches our original.
- The hexagon appears to be oriented differently but same size → OK.
- The square is there.
- The rectangle is there.

But now look at how they fit together.

The rectangle is attached to the square, and the triangle is above the square. But notice that the triangle has one leg aligned with the square, and the hypotenuse pointing up-left.

Is this possible?

Yes — we can rotate the triangle.

But now consider: Does the hexagon fit snugly?

In Figure A, the hexagon is placed such that one side is touching the triangle and another side touches the rectangle. But the hexagon has six sides, and its shape doesn't naturally fit between a triangle and a rectangle unless specific angles align.

Wait — more importantly, let's look at sizes.

The rectangle in the original is long and thin — looks about twice as long as the square is wide.

In Figure A, the rectangle is only as long as the square plus some extra, but not much longer.

But here's a key issue:

In Figure A, the rectangle is shorter than the original rectangle.

Wait — actually, let's compare proportions.

Looking closely:

- The original rectangle is approximately 2 units long by 1 unit high.
- The square is 1x1.
- In Figure A, the rectangle appears to be about the same length as the square, which would make it too short.

So the rectangle in A is too short compared to the original.

Therefore, A is invalid — it uses a resized rectangle.

✘ Eliminate A

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#### Option B:

Now look at Figure B.

- On the left: a large right triangle — seems larger than the original?
- Then a hexagon in the middle.
- A square on the right.
- A long rectangle at the bottom.

Wait — the triangle in B looks larger than the original triangle.

Compare:

- Original triangle: medium-sized right triangle.
- In B, the triangle is much larger, and it's covering a large portion of the figure.

But we cannot resize — so if the triangle is larger, it’s invalid.

Also, the rectangle in B is very long — possibly longer than the original.

But more importantly: Is the triangle the same size?

No — in B, the triangle is clearly larger than the original.

Additionally, the rectangle in B appears to be longer than the original.

So both the triangle and rectangle appear resized.

✘ Eliminate B

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#### Option C:

Now check Figure C.

- On the left: a hexagon
- Then a square
- Then a rectangle
- And a triangle on top of the rectangle

Let’s check each shape:

1. Hexagon: Same size and shape as original → ✔
2. Square: Small square, same size → ✔
3. Rectangle: Long and narrow — matches original → ✔
4. Triangle: Right triangle, rotated — appears same size → ✔

Now, check if they fit together without gaps or overlaps.

- Hexagon is on the far left.
- Square is adjacent to the right of the hexagon.
- Rectangle is to the right of the square.
- Triangle is on top of the rectangle.

Now, check alignment:

- The hexagon has a flat side facing right — does it connect to the square?
- Yes, one side of the hexagon is straight, and the square is placed flush against it.
- The square connects to the rectangle — both have matching sides.
- The triangle is placed on top of the rectangle — its base matches the width of the rectangle?

Wait — the rectangle is long and narrow — say width = 2 units.

The triangle has a base — does it match?

Look at the triangle in C: its base is equal to the width of the rectangle, and it’s placed directly on top.

But the original triangle — its base appears shorter than the rectangle.

Wait — let’s compare sizes carefully.

In the original image:
- The rectangle is longer than the triangle’s base.
- In Figure C, the triangle’s base appears equal to the rectangle’s width.

But in the original, the triangle has a base shorter than the rectangle’s length.

So if the triangle is placed on top of the rectangle, and the base of the triangle is equal to the rectangle’s width, then it should be okay — as long as the triangle is not stretched.

But wait — in Figure C, the triangle is rotated, and its base is horizontal, and it sits on top of the rectangle.

But the rectangle is longer than the triangle’s base, so the triangle only covers part of the rectangle.

That’s fine — no problem.

But now, does the triangle fit over the rectangle?

Yes — the base of the triangle matches the width of the rectangle.

Now, check the hexagon and square.

The hexagon has a flat side — and it connects to the square.

But the square is small — and the hexagon has sides that are likely the same length as the square’s side.

But in Figure C, the hexagon is attached to the square — is the side length consistent?

Yes — the side of the hexagon appears to match the side of the square.

Now, the rectangle is attached to the square — its height matches the square’s side.

And the triangle is on top of the rectangle — its base matches the rectangle’s width.

So all shapes are used, not resized, and fit together.

But wait — is there any overlap or gap?

No — all pieces seem to touch properly.

But let’s double-check the triangle.

In the original, the triangle has a hypotenuse and two legs.

In Figure C, the triangle is placed with its base on the rectangle, and the height going upward.

Its base is horizontal, and the legs go up and to the side.

But the base must be equal in length to the width of the rectangle.

From visual inspection, the rectangle is about twice as long as the square, and the triangle’s base is about the same as the square’s side.

But the rectangle’s width is equal to the square’s side, so the triangle fits.

Wait — is the rectangle’s width equal to the square’s side?

Yes — in Figure C, the rectangle is sitting next to the square, and their heights match — so the rectangle’s height equals the square’s side.

But the rectangle’s width is longer — it’s long and narrow.

So the rectangle is wider than the square.

But in Figure C, the triangle is placed on top of the rectangle, and its base is equal to the rectangle’s width.

But the original triangle — is its base as long as the rectangle’s width?

Looking back at the original image:

- The rectangle is long — visually, it’s about twice as long as the square.
- The triangle’s base is shorter than the rectangle — maybe about the same as the square.

So if the triangle’s base is only as long as the square, but the rectangle is twice as long, then placing the triangle on top of the rectangle would mean the triangle only covers half of the rectangle’s width.

But in Figure C, the triangle is placed on top of the rectangle, and its base appears to cover the entire width of the rectangle.

Wait — that suggests the triangle’s base is as long as the rectangle’s width.

But in the original, the rectangle is longer than the triangle’s base.

So if the triangle’s base is shorter, it cannot cover the full width of the rectangle.

But in Figure C, it does cover the full width — so the triangle must be wider.

This implies resizing — contradiction.

So perhaps C is invalid?

Wait — maybe I’m misjudging.

Let me re-express:

Let’s assign approximate sizes.

Assume the square has side length 1.

Then:

- The rectangle is 2 units long, 1 unit high.
- The triangle: right triangle, legs — one leg appears to be 1 unit, the other maybe 1 unit or less.
- So base ≈ 1 unit.
- The hexagon: regular, side length ≈ 1 unit.

Now in Option C:

- The rectangle is 2 units long, 1 unit high.
- The triangle is placed on top of the rectangle — its base is 2 units long? But the original triangle only has a base of ~1 unit.

So unless the triangle is stretched, it cannot have a base of 2 units.

But in Figure C, the triangle’s base appears to be equal to the rectangle’s width, i.e., 2 units.

But the original triangle is smaller.

So the triangle in C is larger — it’s been resized.

Therefore, C is invalid?

But wait — maybe I’m wrong.

Let’s look again.

Actually, in Figure C, the triangle is placed on top of the rectangle, but its base is not the full width of the rectangle?

Wait — no, it appears to be.

But let’s look at the original triangle.

It’s a right triangle, and it’s smaller than the rectangle.

In Figure C, the triangle is larger — it extends beyond the rectangle.

Wait — no, it’s placed on top — but the base is aligned with the top edge of the rectangle.

But the rectangle is long, and the triangle’s base is shorter.

So if the triangle is placed on top, it should only cover part of the rectangle.

But in Figure C, the triangle appears to cover the entire width of the rectangle.

So unless the triangle is wider, it won’t fit.

But the original triangle is narrower.

So C cannot be made without resizing.

But wait — maybe the triangle is rotated, and its hypotenuse is down?

No — in Figure C, the triangle is placed with its base horizontal, and it’s on top of the rectangle.

But its base must be equal to the rectangle’s width.

But the original triangle has a shorter base.

So C is invalid.

But then none work?

Wait — maybe I missed something.

Let’s go back.

Perhaps Option A is correct?

Earlier I thought the rectangle in A was too short.

But let’s reconsider.

In Option A:

- The rectangle is attached to the square — it’s horizontal, and its length appears to be equal to the square’s side.

But the original rectangle is long and narrow — meaning it’s longer than it is wide.

In Figure A, the rectangle is only as long as the square, so it’s too short.

So A is invalid.

B: triangle is too big — invalid.

C: triangle is too wide — invalid.

But that can’t be — one must be correct.

Wait — perhaps I’ve misjudged Option C.

Let’s look again.

In Option C:

- The hexagon is on the left.
- Then the square.
- Then the rectangle.
- Then the triangle is placed on top of the rectangle, but only partially?

Wait — no — the triangle is placed on top of the rectangle, and its base is equal to the rectangle’s width.

But the rectangle is long, and the triangle’s base is shorter.

Unless the rectangle is short, but it’s not.

Wait — maybe the rectangle in the original is short?

No — in the original, the rectangle is long and narrow, so it’s longer than the square.

In Option C, the rectangle is long, but the triangle is wide.

But the original triangle is not wide.

Wait — perhaps the triangle in C is rotated, and its leg is vertical?

No — it’s placed with the base on the rectangle.

But let’s think differently.

Maybe the triangle in C is not based on the rectangle’s width.

Wait — look at the top of the rectangle — the triangle is sitting on it, and its base is aligned with the rectangle’s top edge.

So the base of the triangle must be equal to the width of the rectangle.

But the original triangle has a base that is shorter than the rectangle’s length.

But the rectangle’s width is its height, which is equal to the square’s side.

So the rectangle is 1 unit high, 2 units long.

The triangle has a base of 1 unit, so it can sit on the rectangle, but only covering half of its length.

But in Figure C, the triangle is placed centered on the rectangle?

But the rectangle is long, and the triangle is small — it would not cover the entire width.

Wait — no — the width of the rectangle is 1 unit, and the triangle’s base is 1 unit, so it can fit.

Ah! That’s the key.

The rectangle has a width of 1 unit (its height), and a length of 2 units.

The triangle has a base of 1 unit, so it can sit on top of the rectangle — covering the entire width, but only part of the length.

But in Figure C, the triangle is placed on the right end of the rectangle — so it sits on the last 1 unit of the rectangle.

But the rectangle is 2 units long, so the triangle is on the right half.

But that’s fine — no need to cover the whole length.

Now, the hexagon is on the left.

The square is next to the hexagon.

The rectangle is next to the square.

So the sequence is: hexagon → square → rectangle (all in a row).

The triangle is on top of the rectangle.

Now, check if all shapes are used:

- Hexagon: yes
- Square: yes
- Rectangle: yes
- Triangle: yes

Are they resized?

- Hexagon: same size — ✔
- Square: same — ✔
- Rectangle: same — ✔
- Triangle: same — ✔

Are they connected properly?

- Hexagon and square: share a side — ✔
- Square and rectangle: share a side — ✔
- Triangle and rectangle: triangle base on top of rectangle — ✔

Is there any overlap or gap?

No — all pieces fit.

But wait — in the original, the triangle is not the same orientation — but rotation is allowed.

So Option C seems valid.

But earlier I thought the triangle’s base was too long — but no, the rectangle’s width is 1 unit, and the triangle’s base is 1 unit, so it fits.

In Figure C, the triangle is placed on the right end of the rectangle, and its base is 1 unit, which matches the rectangle’s height.

So it fits perfectly.

Now, what about Option A?

In A, the rectangle is attached horizontally to the square, but its length is only about the same as the square’s side, so it’s too short.

Original rectangle is long, so A is invalid.

B: the triangle is much larger — clearly resized — invalid.

So only C is valid.

But wait — in Option C, the hexagon is attached to the square, but the hexagon has a flat side, and the square has a side.

But in a regular hexagon, the side length is equal to the distance between opposite sides.

So if the square has side 1, and the hexagon has side 1, then they can fit.

But in Figure C, the hexagon is attached to the square — is the side of the hexagon equal to the side of the square?

Yes — visually, they match.

Similarly, the rectangle is attached to the square — its height is 1, same as square.

So all connections are valid.

Therefore, Option C is the only one that uses all shapes correctly, without resizing.

✔ Answer: C

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Final Answer: C ✔