Area, Perimeter and volume grade 6 worksheet - Free Printable

Let’s solve each problem step by step.

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Problem 1: What is the perimeter of a square with a side of 3 cm?

A square has 4 equal sides.
Perimeter = side + side + side + side = 4 × side
So, 4 × 3 cm = 12 cm

✔ Correct answer: d 12 cm

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Problem 2: What is the area of a square with a side of 4 cm?

Area of a square = side × side
So, 4 cm × 4 cm = 16 cm²

✔ Correct answer: a 16 cm²

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Problem 3: What is the perimeter of this shape?

The shape looks like an “L” made from rectangles. We are given:

- Total bottom length = 8 cm
- Left height = 3 cm
- Right small part height = 2 cm
- Top right horizontal part = 3 cm

We need to add up all the outer edges.

Let’s trace the perimeter:

Start at bottom left corner and go clockwise:

1. Bottom edge: 8 cm
2. Right vertical edge (small part): 2 cm
3. Top-right horizontal edge: 3 cm
4. Vertical drop down inside the L-shape: This is the difference between left height (3 cm) and right height (2 cm) → 1 cm
5. Horizontal leftward on top of the big rectangle: The total width is 8 cm, and we already used 3 cm on the right, so this part is 8 - 3 = 5 cm
6. Left vertical edge going up: 3 cm

Wait — let me double-check that. Actually, when tracing the *outer* perimeter, we don’t go inside. Let’s redraw mentally:

Actually, better way: use the “rectangle trick”.

This L-shape can be thought of as having the same perimeter as a full rectangle if you push out the indented parts.

But let’s do it manually:

Label all outer sides:

- Bottom: 8 cm
- Right side: 2 cm (the short vertical)
- Then move left along the top of the right part: 3 cm
- Then go UP vertically for the gap: since left side is 3 cm tall and right is only 2 cm, there’s a 1 cm rise here → +1 cm
- Then go left across the top of the main block: total width is 8 cm, minus the 3 cm we already went on the right → 5 cm
- Then go down the left side: 3 cm

Now add them:

8 (bottom)
+ 2 (right vertical)
+ 3 (top right horizontal)
+ 1 (vertical rise inside) ← wait, no! That’s not outer perimeter.

I think I messed up. Let’s try again carefully.

Actually, in perimeter problems like this, even if it's indented, you still count every outer edge.

Imagine walking around the outside:

Start at bottom-left corner:

→ Go right along bottom: 8 cm

→ Go up the rightmost edge: 2 cm

→ Go left along the top of the right protrusion: 3 cm

→ Now, instead of going down, we go UP? No — actually, after going left 3 cm, we hit the inner corner. From there, we must go UP to reach the top of the taller part. How much? The left side is 3 cm high, the right part is only 2 cm high, so we go up 1 cm.

→ Then go left along the top of the tall part: how long? Total width is 8 cm, and we’ve already covered 3 cm on the right, so this top segment is 8 - 3 = 5 cm

→ Then go down the left side: 3 cm

→ And back to start? Wait, we’re already at the bottom-left? No — we ended at the top-left after going down 3 cm? Confusing.

Better approach: list ALL outer segments without missing any.

Draw imaginary lines:

Total horizontal movements:

- Bottom: 8 cm (right)
- Top-right horizontal: 3 cm (left)
- Top-left horizontal: 5 cm (left) → because 8 - 3 = 5
→ But these are in opposite directions, but for perimeter, we just add lengths, not vectors.

Vertical movements:

- Right side: 2 cm (up)
- Inner vertical rise: 1 cm (up) — from the 2cm level to 3cm level
- Left side: 3 cm (down)

Wait — direction doesn't matter; we just sum absolute lengths.

So:

Horizontal parts:

- Bottom: 8 cm
- Top-right: 3 cm
- Top-left: 5 cm
→ Total horizontal = 8 + 3 + 5 = 16 cm? But that counts both top and bottom? No — in perimeter, we have two horizontal runs on top? Actually, no.

Let me label points:

Call the shape:

Bottom-left: A
Bottom-right: B
Up to C (2 cm up from B)
Left to D (3 cm left from C)
Up to E (1 cm up from D) — now at same height as left side
Left to F (5 cm left from E) — reaches above A
Down to A (3 cm down)

So path: A → B → C → D → E → F → A

Lengths:

A→B: 8 cm
B→C: 2 cm
C→D: 3 cm
D→E: 1 cm
E→F: 5 cm
F→A: 3 cm

Add them: 8 + 2 + 3 + 1 + 5 + 3 = 22 cm

Yes! So perimeter is 22 cm.

✔ Correct answer: b 22 cm

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Problem 4: A cube has a volume of 64 cm³. What is the length of an edge of the cube?

Volume of cube = edge × edge × edge = edge³

So, edge³ = 64

What number cubed equals 64?

Try:

2³ = 8
3³ = 27
4³ = 64 ← yes!

So edge = 4 cm

✔ Correct answer: d 4 cm

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Final Answer:
1. d
2. a
3. b
4. d