Grade 6 Area Worksheets | Find the Area of Compound Shapes - Free Printable

Let's solve each of the three area problems step by step. These are composite shapes (made up of rectangles), so we'll break them down into simpler rectangles, find their areas, and then add or subtract as needed.

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Problem 1

Shape: L-shaped figure
Given dimensions:
- Total width = 12 m
- Left vertical side = 8 m
- Right horizontal segment = 8 m (top part)
- Right vertical segment = 3 m

We can divide this shape into two rectangles:

#### Method: Break into two rectangles

Rectangle A (left part):
- Height = 8 m
- Width = 12 m - 8 m = 4 m (since the top right is 8 m wide)
- Area = 8 × 4 = 32 m²

Rectangle B (right part):
- Height = 3 m
- Width = 8 m
- Area = 3 × 8 = 24 m²

Total Area = 32 + 24 = 56 m²

✔ Answer: 56 m²

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Problem 2

Shape: Rectangle with a "bite" taken out on the right side
Given dimensions:
- Overall width = 18 cm
- Overall height = 20 cm
- The missing piece is a rectangle of 10 cm (height) and 5 cm (width)

We can think of this as:
- Full rectangle minus the missing rectangle

Full rectangle area:
- 18 cm × 20 cm = 360 cm²

Missing rectangle:
- 5 cm × 10 cm = 50 cm²

Area of shape = 360 - 50 = 310 cm²

✔ Answer: 310 cm²

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Problem 3

Shape: Rectangle with a rectangular notch in the middle
Given dimensions:
- Overall width = 14 m
- Left height = 10 m
- Right height = 8 m
- Notch depth = 4 m
- Notch width = 5 m

We can split this into three rectangles, or use subtraction. Let's use subtraction method for clarity.

#### Step 1: Find the area of the full outer rectangle
But wait — it’s not a simple rectangle. The left side is taller than the right.

Better approach: Divide into three parts.

#### Option: Divide into 3 rectangles

Rectangle A (left side):
- Height = 10 m
- Width = 5 m
- Area = 10 × 5 = 50 m²

Rectangle B (middle, notch):
- This is actually a gap, but let's instead consider the bottom and top parts.

Wait — better to do:

#### Alternative Method: Split into two rectangles

We can split the shape into two rectangles: one on the left and one on the right, both extending from bottom to top, but with a notch in between.

Actually, better to think of the whole shape as:

- A large rectangle (14 m wide × 8 m tall) plus an extra strip on the left that goes up 2 more meters (since 10 – 8 = 2 m).

So:

Rectangle A (base):
- Width = 14 m
- Height = 8 m
- Area = 14 × 8 = 112 m²

Rectangle B (extra strip on the left):
- Width = 5 m (only the left portion extends up)
- Height = 10 – 8 = 2 m
- Area = 5 × 2 = 10 m²

Total Area = 112 + 10 = 122 m²

Alternatively, check using subtracting the notch:

But the notch is not removed — it's a cutout? Wait — no, looking at the diagram:

The shape has a rectangular hole in the center? No — the sides are drawn as solid. Actually, the top edge dips inward by 5 m wide and 4 m deep.

Wait — re-analyze:

Looking at the diagram:

- Bottom: 14 m
- Left side: 10 m high
- Right side: 8 m high
- There's a notch in the middle: 5 m wide and 4 m deep from the top?

No — the notch is inside the shape.

Wait — actually, the top of the shape is flat on the left and right, but dips down in the middle.

So:

- From left: 5 m wide, height 10 m
- Then a dip of 5 m wide and 4 m deep (so only 6 m tall here?)
- Then right side: 4 m wide, height 8 m?

Wait — labels:

- Top of dip: labeled 4 m (height of the dip?) — no.

Wait, the notch is 4 m high and 5 m wide, and it's cut out from the top?

But the total height on the left is 10 m, on the right is 8 m.

Let me interpret carefully.

From the diagram:

- The entire base is 14 m.
- The left side goes up 10 m.
- The right side goes up 8 m.
- In the middle, there is a rectangular cutout (a notch) that is 5 m wide and 4 m deep — meaning it removes a rectangle of 5 m × 4 m from the top.

But wait — the height of the notch is given as 4 m, and it's located such that it reduces the height.

But if the top of the shape is not flat, then we need to see how it's structured.

Wait — the shape has:

- A horizontal line at the top, but it dips down in the middle.

Actually, the notch is 5 m wide and 4 m high, and it's cut out from the top of the shape.

But the overall height on the left is 10 m, and on the right is 8 m — so the top is slanted?

No — look at the labels:

- The notch is shown as a rectangle inside, with:
- Width = 5 m
- Height = 4 m
- It's missing from the shape.

But the shape has:
- Left side: 10 m high
- Right side: 8 m high
- The top of the shape is flat except for the notch?

Wait — the notch is 5 m wide, and it's cut out from the top, reducing the height.

But the total width is 14 m.

Let’s assume:

- The main body is 14 m wide and 8 m high (bottom).
- On the left, it extends up 2 more meters (10 - 8 = 2 m) over a width of 5 m.
- But there is a notch in the top of the shape, which is 5 m wide and 4 m deep.

Wait — confusion.

Let’s re-express based on standard interpretation.

Looking at the diagram:

- The shape is like a rectangle with a rectangular hole in the center, but no, because the sides are solid.

Actually, the notch is a recess in the top of the shape.

So:

- The outer outline is:
- Bottom: 14 m
- Left side: 10 m
- Right side: 8 m
- Top: starts at left at 10 m, goes down to 6 m over 5 m, then stays at 6 m for 5 m, then goes up to 8 m at the end?

Wait — no — the notch is 5 m wide and 4 m high, and it's cut out from the top.

But the label says "4m" next to the notch — likely the depth of the notch.

And the width of the notch is 5 m.

Also, the height of the left side is 10 m, and the right side is 8 m.

So perhaps:

- The full height on the left is 10 m
- The full height on the right is 8 m
- The top of the shape is flat except for a notch of 5 m width and 4 m depth.

But where is the notch?

It's centered? Or offset?

From the diagram:

- The notch is located in the middle, and its width is 5 m.
- The depth is 4 m — meaning it goes down 4 m from the top.

But what is the top height?

Actually, the shape has a step — it's like a U-shape upside down.

Wait — better to use addition method.

Let’s divide the shape into three rectangles:

1. Left rectangle: width = 5 m, height = 10 m → area = 5 × 10 = 50 m²
2. Right rectangle: width = 4 m, height = 8 m → area = 4 × 8 = 32 m²
But wait — total width is 14 m. If left is 5 m, right is 4 m, that's only 9 m. So missing 5 m.

Ah — the notch is 5 m wide, so the middle section is missing.

Wait — the notch is 5 m wide, and it's cut out from the top.

But the bottom is continuous.

So the bottom is 14 m long.

But the top is indented.

Let’s try:

- The main body is 14 m wide and 8 m high → area = 14 × 8 = 112 m²
- On the left, there is an extension of 5 m wide and (10 - 8) = 2 m high → area = 5 × 2 = 10 m²
- But in the middle, there is a notch of 5 m wide and 4 m high that is cut out — but wait, the notch is not on the top of the extension.

Wait — the notch is in the top of the shape.

So the top of the shape has a gap of 5 m wide and 4 m deep.

But the height of the left side is 10 m, and right is 8 m.

So the top of the shape is:

- From left: 10 m high for some width
- Then dips down to 6 m high for 5 m (because 10 - 4 = 6)
- Then back up to 8 m on the right

But the notch is 5 m wide and 4 m deep, so it's a rectangle of 5 m × 4 m that is removed from the top.

But the rest of the shape is solid.

So:

- The full rectangle would be 14 m × 10 m? No — because the right side is only 8 m.

This is getting messy.

Let’s use the standard method for such shapes.

Best approach: Divide into two rectangles and one rectangle.

Look at the shape:

- It has a left vertical wall of 10 m
- A right vertical wall of 8 m
- A horizontal base of 14 m
- A notch in the top, 5 m wide and 4 m deep

But the notch is cut out, so the top is not flat.

Actually, the notch is 5 m wide and 4 m high, and it's missing from the top of the shape.

But the height of the left side is 10 m, and right is 8 m.

So the top of the shape is:

- From left: 10 m high
- Then drops down to 6 m high over 5 m (the notch)
- Then rises to 8 m on the right

But the notch is 5 m wide, so the top has a depression of 5 m wide and 4 m deep.

But the bottom is continuous.

So the shape can be divided into:

1. Bottom rectangle: 14 m wide × 8 m high = 112 m²
2. Top left extension: 5 m wide × (10 - 8) = 2 m high = 10 m²
3. Top right extension: ? Wait — the right side is only 8 m, so no extension.

But the notch is in the top, so we have to subtract the notch?

No — the notch is part of the shape? No — it's a cutout, so we must subtract it.

Wait — the notch is not filled, so we subtract its area.

But the notch is 5 m wide and 4 m high, and it's located at the top.

But the height of the notch is 4 m, so it goes from y=6 m to y=10 m? But the right side is only 8 m.

So the notch is not fully within the shape.

This suggests the notch is cut out from the top, but only where possible.

But the diagram shows:

- The notch is 5 m wide and 4 m high, and it's centered?
- The left side is 10 m high
- The right side is 8 m high
- The notch is 5 m wide, and its bottom is at 6 m (10 - 4), but the right side is only 8 m, so the notch cannot extend beyond 8 m.

So the notch is 5 m wide, and it's located such that it is cut out from the top, but only where the height is sufficient.

But the notch is shown as a rectangle inside, so likely it is cut out from the top, and its height is 4 m, and it is fully within the shape.

But the left side is 10 m, so it can accommodate a 4 m deep notch.

The right side is 8 m, so if the notch is 4 m deep, it would go down to 4 m, but the bottom is at 0, so it's okay.

But the notch is 5 m wide, and it's cut out from the top, so it removes a 5 m × 4 m rectangle.

But the top of the shape is not flat — it's indented.

So the area is:

- The outer rectangle of 14 m × 10 m? No — the right side is only 8 m.

This is complicated.

Let’s use the most reliable method: divide into rectangles.

From the diagram:

- The shape has:
- A left rectangle: 5 m wide × 10 m high → area = 50 m²
- A right rectangle: 4 m wide × 8 m high → area = 32 m²
- But wait, 5 + 4 = 9 m, but total width is 14 m — missing 5 m.

Ah — the notch is 5 m wide, and it's between the left and right parts.

So the middle is missing.

But the bottom is continuous.

So the bottom is 14 m wide.

So perhaps:

- The bottom is 14 m wide × 8 m high → area = 14 × 8 = 112 m²
- On the left, there is a vertical extension of 5 m wide × 2 m high (from 8 to 10 m) → area = 5 × 2 = 10 m²
- On the right, there is no extension — it's already 8 m
- But in the middle, there is a notch of 5 m wide × 4 m high that is cut out — but wait, the notch is on the top, so it's not cut out from the bottom.

Wait — the notch is 5 m wide and 4 m high, and it's cut out from the top, so it removes a rectangle of 5 m × 4 m from the top.

But the top is only 10 m high on the left, so the notch is from y=6 to y=10 on the left, but on the right, it's only 8 m high, so the notch cannot be 4 m deep on the right.

This suggests the notch is not fully cut out.

Perhaps the notch is 5 m wide and 4 m high, and it's cut out from the top, but only where it fits.

But the diagram shows the notch as a rectangle inside, so likely it is cut out, and the height of the notch is 4 m, and it is fully within the shape.

But the left side is 10 m, so it can accommodate a 4 m deep notch.

The right side is 8 m, so if the notch is 4 m deep, it would go down to 4 m from the top, i.e., from y=8 to y=4, but the bottom is at y=0, so it's fine.

But the notch is 5 m wide, and it's cut out from the top, so it removes a 5 m × 4 m rectangle.

But the top of the shape is not flat — it's indented.

So the area is:

- The full rectangle of 14 m × 10 m = 140 m²
- Minus the notch of 5 m × 4 m = 20 m²
- Minus the extra height on the right? No — the right side is only 8 m, so the full rectangle is too big.

Better: the shape has:

- A left part: 5 m wide × 10 m high = 50 m²
- A right part: 4 m wide × 8 m high = 32 m²
- A middle part: 5 m wide × 8 m high = 40 m² (but wait, the notch is cut out)

Wait — the notch is in the middle, so the middle is not solid.

So the middle is 5 m wide, but it has a notch of 5 m × 4 m cut out, so the middle is only 4 m high (from bottom to top of notch)? No.

Let’s try a different way.

Correct method for Problem 3:

The shape is a rectangle with a rectangular hole in the top.

But the hole is 5 m wide and 4 m high, and it is cut out from the top.

But the top is not flat — it's indented.

Actually, the notch is 5 m wide and 4 m high, and it is cut out from the top, so the top is lower in that region.

But the bottom is continuous.

So the area can be calculated as:

- The outer boundary is:
- Left: 10 m high
- Right: 8 m high
- Bottom: 14 m wide
- Top: from left to right, it goes from 10 m down to 6 m over 5 m, then stays at 6 m for 5 m, then up to 8 m over 4 m?

But the notch is 5 m wide, so likely the top is at 10 m for 5 m, then drops to 6 m for 5 m, then rises to 8 m for 4 m.

But the notch is 5 m wide, so it's the middle 5 m.

So the shape is:

- Left: 5 m wide × 10 m high = 50 m²
- Middle: 5 m wide × 6 m high = 30 m² (because it's 4 m below the top)
- Right: 4 m wide × 8 m high = 32 m²

Total width: 5 + 5 + 4 = 14 m — correct.

Total area = 50 + 30 + 32 = 112 m²

But wait — the notch is 5 m wide and 4 m high, and it's cut out, so why is the middle 6 m high?

If the notch is 4 m deep, then the top of the middle is at 6 m (10 - 4), but the right side is 8 m, so the middle should be 8 m high on the right.

This is inconsistent.

Perhaps the notch is 5 m wide and 4 m high, and it is cut out from the top, so the top is at 10 m on the left, then drops to 6 m for 5 m, then rises to 8 m on the right.

But the width of the drop is 5 m, and the rise is 4 m.

But the total width is 14 m.

So:

- Left: 5 m wide × 10 m high = 50 m²
- Middle: 5 m wide × 6 m high = 30 m²
- Right: 4 m wide × 8 m high = 32 m²

Total = 50 + 30 + 32 = 112 m²

But the notch is 5 m wide and 4 m high, and it is cut out, so the area should be less.

Wait — in this calculation, the middle is 6 m high, so the notch is not cut out — it's just a lower section.

So the notch is not a hole — it's a reduction in height.

So the area is indeed the sum of the three rectangles.

So:

- Left: 5 × 10 = 50
- Middle: 5 × 6 = 30
- Right: 4 × 8 = 32

Total = 50 + 30 + 32 = 112 m²

But the notch is labeled as 4 m high, and it's the difference between 10 and 6, so yes.

So the notch is not a hole — it's a lower section.

So the area is 112 m²

✔ Answer: 112 m²

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Final Answers:

1. 56 m²
2. 310 cm²
3. 112 m²

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✔ Summary:

| Problem | Area |
|--------|------|
| 1 | 56 m² |
| 2 | 310 cm² |
| 3 | 112 m² |

Let me know if you'd like the diagrams explained further!