Grade 6 Area and Perimeter Worksheets | Free Math Worksheets - Free Printable

Let's solve each of the three composite shapes step by step and find their areas.

---

Problem 1:

Shape: A diamond-like figure with a rectangle in the middle.

We can see:
- The full shape looks like a rhombus or two triangles on either side of a rectangle.
- The central rectangle is 3m wide and 12m high.
- On each side, there’s a triangle with a base of 6cm, but wait — units don't match!

Wait — this is a problem. The rectangle is labeled 12m, and the width is 3m, but the horizontal dashed line is labeled 6cm.

This is likely a unit inconsistency. But looking closely:

- The vertical height is 12m
- The base of the right triangle is 6cm → that seems inconsistent.

But let’s assume it's a typo and the 6cm should be 6m, because otherwise, the dimensions are mismatched.

So, we'll assume:
- The total horizontal length across the center is 6m, so each triangle has a base of 6m / 2 = 3m? Wait, no — the diagram shows a dashed line of 6cm, which might mean the total horizontal span is 6 cm?

Wait — again, units conflict: 12m vs 6cm.

But more likely, the 6cm is a typo, and it should be 6m, or vice versa.

Looking at the drawing:
- The central rectangle is 3m wide, and 12m tall.
- The two side triangles extend horizontally from the rectangle, and the dashed line (which appears to be the total width) is labeled 6cm — but this doesn’t make sense with 12m.

Alternatively, perhaps the 6cm is meant to be 6m, and the 12m is the height.

Let’s reinterpret carefully.

Actually, the shape appears to be a diamond split vertically into a rectangle and two triangles.

But the height is 12m, and the width of the rectangle is 3m, and the horizontal extension on the sides is 6cm — again, units don’t match.

Wait — maybe the 6cm is a mistake, and it's actually 6m?

Alternatively, could the 12m be 12cm?

But let's look at the other problems: they use cm and m, so probably not.

Alternatively, perhaps the 6cm is a typo and should be 6m.

Let’s suppose all units are meters, and 6cm is a typo for 6m.

So:
- The central rectangle is 3m wide × 12m tall.
- On each side, there is a triangle with base = 6m and height = 12m? No — that would make the total width 3 + 6 = 9m, but the dashed line is only 6m.

Wait — the dashed line goes from left to right across the top, and is labeled 6cm, but the rectangle is 3m wide.

Perhaps the 6cm is meant to be 6m, and the rectangle is 3m wide, so the two side triangles have a combined base of 6m - 3m = 3m? That doesn’t make sense.

Wait — the dashed line appears to be the full horizontal width of the shape, and it’s labeled 6cm.

But the rectangle is 3m wide, and 12m tall.

This is impossible unless the 6cm is 6 meters.

So, likely, 6cm is a typo, and it should be 6m.

Assume:
- The full horizontal width is 6m
- The central rectangle is 3m wide and 12m tall
- So, on each side, there is a triangle with base = (6m - 3m)/2 = 1.5m, and height = 12m

But wait — the shape looks symmetric, and the dashed line is horizontal across the top, and labeled 6cm, but the vertical dimension is 12m.

Alternatively, perhaps the 12m is the height of the rectangle, and the 6cm is the horizontal distance from the center to the edge.

Wait — another idea: the dashed line is the diagonal of the rhombus?

No — it’s drawn horizontally through the center.

Let me try a different interpretation.

The shape looks like a rhombus made of a central rectangle and two triangles on the sides.

But the rectangle is 3m wide, and 12m tall.

Then, on the left and right, there are triangles attached to the sides.

But the horizontal dashed line is labeled 6cm — but if the rectangle is 3m wide, and the total width is 6m, then the two side triangles must each have a base of (6 - 3)/2 = 1.5m, and height = 12m?

But the triangle is attached to the side of the rectangle, so its height would be along the length of the rectangle?

Wait — the rectangle is 12m tall, and 3m wide.

The dashed line is horizontal, going from left to right, and labeled 6cm — but if the rectangle is 3m wide, and the total width is 6m, then the side triangles must each be 1.5m wide.

But the triangle is attached to the side, so its base is 1.5m, and its height is 12m?

Yes — that makes sense.

But units: 12m, 3m, 6cm — 6cm is likely a typo for 6m.

So we’ll assume:
- Total horizontal width = 6m
- Central rectangle: 3m wide × 12m tall
- Each side triangle: base = (6 - 3)/2 = 1.5m, height = 12m

But wait — if the triangle is attached to the side, then its height is along the vertical direction, but the rectangle is 12m tall, so the triangle extends horizontally out from the side.

So yes, the triangle has:
- Base = 1.5m (horizontal)
- Height = 12m (vertical)

But that would make the area of one triangle = (1/2) × base × height = (1/2) × 1.5 × 12 = 9 m²

Two triangles: 18 m²

Rectangle: 3 × 12 = 36 m²

Total area = 36 + 18 = 54 m²

But wait — is the triangle really extending vertically? No — the triangle is attached to the side of the rectangle, so its height is horizontal, and its base is vertical?

Wait — confusion in orientation.

Let’s redraw mentally:

- The rectangle is vertical: 12m tall, 3m wide.
- On the left and right sides, there are triangles extending outward.
- The dashed line is horizontal across the top, labeled 6cm — but if the total width is 6m, and the rectangle is 3m, then each triangle extends 1.5m out.

So the base of each triangle is 1.5m (horizontal), and the height is 12m (vertical), since it spans the full height of the rectangle.

So area of one triangle = (1/2) × 1.5 × 12 = 9 m²

Two triangles: 18 m²

Rectangle: 3 × 12 = 36 m²

Total area = 36 + 18 = 54 m²

But the label "6cm" is problematic — it should be 6m.

So likely, 6cm is a typo for 6m.

We'll go with that.

✔ Answer for Problem 1: 54 m²

---

Problem 2:

A rectangular L-shape.

Dimensions:
- Overall height: 8cm
- Bottom width: 9cm
- Right side has a step inward: 3cm wide and 3cm high.

So we can think of this as a large rectangle minus a smaller rectangle, or add two rectangles.

#### Method 1: Divide into two rectangles

Option A:
- Left part: 8cm high, 6cm wide (since 9cm total, and 3cm missing on right)
- Right part: 3cm high, 3cm wide

Wait — the step is 3cm high, so the upper right rectangle is 3cm high, and 3cm wide.

The lower right rectangle is (8 - 3) = 5cm high, and 3cm wide.

Better:

Divide into:
- Bottom rectangle: 9cm wide × 5cm high (because top 3cm is cut off)
- Top rectangle: 6cm wide × 3cm high (because 3cm is missing on right)

Wait — total height is 8cm.

The right side has a step down of 3cm.

So:
- The top rectangle is 6cm wide (9 - 3) and 3cm high
- The bottom rectangle is 9cm wide and 5cm high (8 - 3)

Area = (6 × 3) + (9 × 5) = 18 + 45 = 63 cm²

Alternatively:
- Whole rectangle: 9 × 8 = 72 cm²
- Missing rectangle: 3 × 3 = 9 cm² (the corner missing)
- Area = 72 - 9 = 63 cm²

✔ Answer for Problem 2: 63 cm²

---

Problem 3:

Another L-shaped figure.

Dimensions:
- Total width: 12m
- Total height: 10m
- There’s a notch in the middle.

From bottom:
- Bottom rectangle: 12m wide × 2m high
- Middle rectangle: 6m wide × 8m high? Wait.

Wait — the figure has:
- A long bottom section: 12m wide, 2m high
- Then above it, a rectangle of 6m wide and 8m high? But the total height is 10m, and 2 + 8 = 10, so yes.

But the top part is only 6m wide, and the middle is 8m high.

But the left side is 10m high, and the right side has a step.

Wait — the top part is 2m high, and the middle is 8m high?

No — look:

- The bottom is 2m high
- Then a middle section of 8m high?
- But total height is 10m — so 2 + 8 = 10, yes.

But the top of the figure is only 2m high, and 8m wide? No.

Wait — labels:
- At the top: a small rectangle of 8m wide × 2m high
- Below it: a rectangle of 6m wide × 8m high? But the total height is 10m.

Wait — the entire height is 10m.

From bottom:
- Bottom rectangle: 12m wide × 2m high
- Middle rectangle: 6m wide × 8m high? But then the top is 2m high.

But the top is labeled as 2m high, and 8m wide, so it’s a rectangle of 8m × 2m.

Then below it, there’s a gap — but no, the shape continues.

Actually, the shape is:
- A large rectangle on the bottom: 12m wide × 2m high
- Above it, a rectangle that is 6m wide × 8m high — but where is it placed?

Wait — the left side is 10m high, and the right side has a step.

From the drawing:
- The bottom is 12m wide × 2m high
- Then, above it, the left part is 6m wide and 8m high
- And the top is 8m wide and 2m high — but that overlaps.

Wait — better:

The shape is like a C or U shape.

From the labels:
- The bottom is 12m wide × 2m high
- The top is 8m wide × 2m high
- The middle is 6m wide × 8m high? But 2 + 8 + 2 = 12, but total height is 10m.

Wait — total height is 10m.

The bottom is 2m high

Then a middle section: 6m wide × 8m high? But that would be 10m total height.

But the top is 2m high, so the middle must be 8m high.

But the top is only 8m wide, so the middle is 6m wide.

So:
- Bottom rectangle: 12m × 2m = 24 m²
- Middle rectangle: 6m × 8m = 48 m²
- Top rectangle: 8m × 2m = 16 m²

Wait — but the top is only 8m wide, and the middle is 6m wide — how do they connect?

Actually, the top is 8m wide and 2m high, and the middle is 6m wide and 8m high, but the middle is offset.

Wait — looking at the diagram:

- The left side is 10m high
- The right side has a step inward at 2m and 8m from bottom
- The top is 8m wide
- The bottom is 12m wide

So the shape consists of:
- A bottom rectangle: 12m wide × 2m high
- A middle rectangle: 6m wide × 8m high (from 2m to 10m height)
- A top rectangle: 8m wide × 2m high

But wait — the middle is only 6m wide, and the top is 8m wide — so the top extends beyond the middle?

No — the top is 8m wide, and the middle is 6m wide, so the top is wider than the middle — but the middle is centered?

Wait — the bottom is 12m wide, the top is 8m wide, and the middle is 6m wide.

But the middle is between them.

So:
- From bottom to 2m: 12m wide → area = 12 × 2 = 24 m²
- From 2m to 8m: 6m wide → height = 6m? But total height is 10m.

Wait — the middle is 8m high? But from 2m to 10m is 8m.

Yes.

So:
- Bottom: 12m × 2m = 24 m²
- Middle: 6m × 8m = 48 m²
- Top: 8m × 2m = 16 m²

But wait — the top is only 2m high, and the middle is 8m high, but the top is on top of the middle?

But the middle is only 6m wide, and the top is 8m wide — so the top must extend over the middle and also over the bottom?

But the bottom is 12m wide, so the top is 8m wide — it fits.

But the middle is 6m wide, so the top is wider than the middle.

But the top is 8m wide, and the middle is 6m wide — so the top extends 1m beyond the middle on each side?

But the bottom is 12m wide, so the top is narrower.

Wait — the top is 8m wide, the middle is 6m wide, and the bottom is 12m wide.

So the top is centered?

But the middle is only 6m wide, so the top cannot be 8m wide unless it extends beyond the middle.

But that would require a horizontal overlap, which is not possible.

Alternative interpretation:

The shape is like a staircase.

From the drawing:
- The bottom is 12m wide × 2m high
- Then a step up of 6m wide × 8m high — but the step is 8m high, so from 2m to 10m
- Then a top of 8m wide × 2m high

But the step is only 6m wide, so the top is 8m wide — so it must be offset.

But the top is 8m wide, and the step is 6m wide — so the top is wider than the step — impossible unless it's not aligned.

Wait — perhaps the top is 8m wide and 2m high, and it sits on top of the step, but the step is 6m wide, so the top is 8m wide — so it must extend 1m beyond on each side.

But the bottom is 12m wide, so the top is narrower.

But the step is 6m wide, so the top is wider than the step — that means the top is not supported.

But geometrically, it's possible.

But let's calculate the area by dividing into rectangles.

Best way: divide into three parts:

1. Bottom rectangle: 12m × 2m = 24 m²
2. Middle rectangle: 6m × 8m = 48 m²
3. Top rectangle: 8m × 2m = 16 m²

But are these non-overlapping?

- The bottom is from y=0 to y=2
- The middle is from y=2 to y=10, x=0 to x=6
- The top is from y=10 to y=12? But total height is 10m.

Wait — the top is 2m high, but the middle is 8m high, from y=2 to y=10.

So the top must be from y=8 to y=10? But it's labeled as 2m high.

Wait — the top is labeled as 2m high, and the middle is 8m high, but the total height is 10m.

So:
- Bottom: 2m high
- Middle: 8m high
- Top: 2m high? But 2+8+2=12 > 10.

No — total height is 10m.

So:
- Bottom: 2m high
- Middle: 8m high
- Top: ? But there is no room.

Wait — the top is labeled as 2m high, and the middle is 8m high, but the total height is 10m.

So the top must be from y=8 to y=10 — 2m high.

And the middle is from y=2 to y=8 — 6m high?

But the label says 8m.

Wait — the middle is labeled as 8m high, and the top is 2m high, and the bottom is 2m high — total 12m.

But the total height is labeled as 10m.

Contradiction.

Wait — the total height is 10m, and the bottom is 2m, the top is 2m, so the middle is 6m high.

But the middle is labeled as 8m?

No — the middle is labeled as 8m in width, not height.

Look:

- The middle rectangle is labeled 8m in width
- The top is labeled 2m in height
- The bottom is labeled 2m in height
- The total height is 10m
- The bottom is 12m wide
- The middle is 8m wide
- The top is 6m wide? No — the top is labeled as 8m wide

Wait — the top is labeled as 8m wide, and 2m high.

The middle is labeled as 8m wide, and 6m high? But the total height is 10m.

Wait — the middle is 6m high, from y=2 to y=8, and the top is 2m high, from y=8 to y=10.

But the middle is labeled as 8m — but that’s the width.

Yes — the middle is 8m wide, and the top is 8m wide, and the bottom is 12m wide.

The heights:
- Bottom: 2m
- Middle: 6m (from y=2 to y=8)
- Top: 2m (from y=8 to y=10)

But the middle is labeled as 8m — but that’s width, not height.

Yes — the 8m next to the middle is the width.

Similarly, the 6m is the width of the step.

Wait — the middle is 8m wide, and the top is 8m wide, but the bottom is 12m wide.

So the middle is 8m wide, and the top is 8m wide, but the bottom is 12m wide.

So the middle is inset.

Now, the heights:
- Bottom: 2m
- Middle: 6m (from y=2 to y=8)
- Top: 2m (from y=8 to y=10)

But the middle is 6m high, not 8m.

But the total height is 10m, and bottom is 2m, top is 2m, so middle is 6m high.

But the label "8m" is the width.

Yes.

So:
- Bottom rectangle: 12m × 2m = 24 m²
- Middle rectangle: 8m × 6m = 48 m²
- Top rectangle: 8m × 2m = 16 m²

But wait — the top is 8m wide, and the middle is 8m wide, so they align.

But the bottom is 12m wide, so the middle is inset.

But the middle is 8m wide, so it's centered?

But the top is also 8m wide.

So the area = 24 + 48 + 16 = 88 m²

But is the middle really 6m high?

Total height: 10m
- Bottom: 2m
- Top: 2m
- Middle: 6m

Yes.

But the label "8m" is for width, not height.

So yes.

Alternatively, we can think of it as:
- The entire shape has a bottom of 12m × 2m
- A middle of 8m × 6m
- A top of 8m × 2m

All stacked.

But the middle is only 8m wide, so it's narrower than the bottom.

So the area is sum: 24 + 48 + 16 = 88 m²

But wait — the top is 8m wide, and the middle is 8m wide, so they are aligned.

Yes.

But the total height is 10m, and 2+6+2=10, good.

So ✔ Answer for Problem 3: 88 m²

---

Final Answers:

1. 54 m²
2. 63 cm²
3. 88 m²

---

Summary:

| Problem | Area |
|--------|------|
| 1 | 54 m² |
| 2 | 63 cm² |
| 3 | 88 m² |

> Note: In Problem 1, the label "6cm" is likely a typo and should be "6m". If not, the units are inconsistent. We assumed it was 6m for consistency.