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

Let’s solve each problem step by step. We’ll break the shapes into rectangles, find the area of each rectangle, and then add them up.

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Problem 1:

The shape is an L-shape. We can split it into two rectangles:

- Rectangle A (left vertical part):
Height = 8m, Width = ?
The total bottom length is 12m, and the right horizontal part is 8m long → so left width = 12m - 8m = 4m
Area = 8m × 4m = 32 m²

- Rectangle B (bottom horizontal part):
Length = 8m, Height = 3m
Area = 8m × 3m = 24 m²

Total Area = 32 + 24 = 56 m²

✔ Double-check: Another way — imagine full rectangle 12m x 8m = 96 m², minus missing top-right rectangle: 8m wide and (8-3)=5m tall → 8×5=40 → 96-40=56. Same answer!

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Problem 2:

Another L-shape. Split into two rectangles:

- Rectangle A (left big rectangle):
Height = 20cm, Width = ?
Total bottom = 18cm, right part = 5cm → left width = 18 - 5 = 13cm
But wait — look at the diagram: the right side has a step down. Actually, better to split horizontally or vertically?

Actually, let’s split it as:

- Top rectangle: height = 10cm, width = 18cm? No — because the right part sticks out only 5cm.

Better approach:

Split into:

- Left rectangle: full height 20cm, width = 18cm - 5cm = 13cm → Area = 20 × 13 = 260 cm²

- Right small rectangle: height = 20cm - 10cm = 10cm, width = 5cm → Area = 10 × 5 = 50 cm²

Wait — that doesn’t match the diagram. Let me re-read.

Diagram says:

- Left side: 20cm tall
- Bottom: 18cm wide
- On the right, there’s a step: from top, down 10cm, then right 5cm, then down to bottom.

So actually, the shape is like:

Full rectangle 18cm x 20cm, but with a notch cut out on the top right? Or built up?

Actually, looking again: It’s a rectangle 18cm wide and 20cm tall, but the top right corner is “cut” — no, wait, the labels show:

From top left, go right some amount, then down 10cm, then right 5cm, then down to bottom.

Actually, the correct split:

Think of it as two rectangles stacked vertically on the left, and one on the right? Maybe easier to do:

Option: Split vertically

- Left part: width = 18cm - 5cm = 13cm, height = 20cm → Area = 13 × 20 = 260 cm²

- Right part: width = 5cm, height = 20cm - 10cm = 10cm → Area = 5 × 10 = 50 cm²

Total = 260 + 50 = 310 cm²

But wait — does that match? The top part on the right is only 10cm high? Yes, because from the top, you go down 10cm before going right 5cm. So the right rectangle is only 10cm tall.

Alternatively, think of the whole thing as:

Big rectangle 18cm x 20cm = 360 cm²

Minus the missing top-right rectangle: which is 5cm wide and 10cm tall → 50 cm²

So 360 - 50 = 310 cm² — same answer! Good.

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Problem 3:

This is a U-shape or something similar. Let’s label the parts.

Total width = 14m

Left side: 10m tall, top segment 5m wide

Then it goes down 5m (so now at 5m height), then right 4m, then up 4m? Wait, diagram says:

From left: 10m down, then right 5m, then down? No — let's read carefully.

Actually, the shape:

- Starts at top left, goes right 5m
- Then down ? — the next label is "5m" under the middle dip — probably meaning the depth of the dip is 5m? But also there’s “4m” labeled on the right inner side.

Looking at the diagram description:

It’s symmetric-ish? Total width 14m.

Left column: 5m wide, 10m tall

Right column: ? wide, 8m tall? Wait, labeled 8m on right side.

Middle: between them, there’s a dip: 5m wide (horizontal) and 4m deep? But also labeled “5m” in the middle bottom.

Actually, let’s reconstruct:

Imagine the shape has:

- Left rectangle: 5m wide × 10m tall

- Right rectangle: let’s say X m wide × 8m tall

- Middle connecting part: but it’s indented.

Total width = 14m

If left is 5m, and right is, say, Y m, and middle gap is Z m, but the middle has a protrusion downward?

Actually, better to split into three rectangles:

1. Left vertical rectangle: 5m wide × 10m tall → Area = 50 m²

2. Right vertical rectangle: how wide? Total width 14m, left is 5m, and the middle horizontal part is 5m wide (labeled in the dip), so right must be 14 - 5 - 5 = 4m? But the right side is labeled 8m tall.

Wait, the right side height is 8m, not 10m.

Also, in the middle, there’s a rectangle sticking down: 5m wide and... how tall? From the top of the dip to bottom.

The left side is 10m, right side is 8m, and the middle dip has a horizontal segment labeled 5m, and a vertical segment labeled 4m on the right inner side.

Perhaps:

The shape can be seen as a large rectangle minus two notches? Or add three parts.

Let me try adding:

- Bottom base rectangle: full width 14m, height = min(10,8) = 8m? But not quite.

Another way:

Divide the shape into:

A. Left tower: 5m × 10m = 50 m²

B. Right tower: let’s find its width. Total width 14m. The middle horizontal part (the bridge) is 5m wide (as labeled in the dip). So if left is 5m, middle bridge is 5m, then right tower is 14 - 5 - 5 = 4m wide. And its height is 8m → Area = 4 × 8 = 32 m²

C. Now, the middle part: between the towers, there is a rectangle that connects them at the bottom? But the dip is 5m wide and how deep?

From the top of the left tower (10m) to the top of the right tower (8m), but they are connected by a horizontal piece at the bottom of the dip.

Actually, looking at the labels: in the middle, there is a horizontal segment labeled "5m" (probably the width of the dip), and a vertical segment labeled "4m" on the right side of the dip — meaning from the top of the right tower down to the bottom of the dip is 4m? But the right tower is 8m tall, so if you go down 4m from top, you’re at 4m above bottom? Confusing.

Perhaps the "4m" is the height of the inner vertical drop.

Let me interpret based on standard such problems.

Commonly, for this shape:

- The overall bounding box is 14m wide and 10m tall (since left is 10m).

- There is a rectangular notch cut out from the top middle.

The notch: width = 5m (labeled in the middle), and height = ?

The right side is 8m, so from top (10m) down to 8m is 2m, but there’s a label "4m" — perhaps the depth of the notch is 4m? But 10 - 4 = 6, not matching.

Wait, the label "4m" is on the right inner vertical side — likely meaning that from the bottom of the shape up to the start of the right tower is 4m? No.

Let’s list all given dimensions clearly from the diagram description:

- Left outer height: 10m

- Top left horizontal: 5m

- Then it goes down — the next horizontal in the middle is labeled "5m" — this is the width of the recessed part.

- Then on the right side of that recess, there’s a vertical segment labeled "4m" — this is probably the height from the bottom of the recess to the bottom of the shape? Or to the top?

Actually, I think the "4m" is the height of the right inner wall — meaning from the bottom of the shape up to where the right tower starts is 4m, but the right tower is 8m tall, so total height on right is 4m + 8m = 12m? But left is only 10m — inconsistency.

Perhaps the "8m" is the total height on the right, and the "4m" is the depth of the dip from the top.

Assume:

The shape has a flat bottom of 14m.

On the left, a rectangle 5m wide × 10m tall.

On the right, a rectangle of width W × 8m tall.

In the middle, between them, there is a rectangle that is 5m wide (as labeled) and height H, but it's lower.

The key is the vertical distances.

From the top of the left side (10m) to the top of the middle dip: since the middle dip has a horizontal part, and then it goes down to connect to the right side.

The label "4m" is on the right inner vertical — likely, it means that the right tower rises 4m from the bottom of the dip to its top, but the right tower's total height is 8m, so the dip must be at 8m - 4m = 4m above bottom? This is messy.

Alternative approach: use the fact that the total width is 14m, and the top has segments.

Top view:

- Left: 5m

- Then a gap (the dip) of 5m wide

- Then right part: 14 - 5 - 5 = 4m wide

Now heights:

- Left part: 10m tall

- Right part: 8m tall

- The middle part: it is recessed. The depth of the recession: from the top level, how far down?

The label "4m" is on the right inner side — probably, it means that from the bottom of the shape to the bottom of the right tower's base is 4m, but that doesn't make sense.

Perhaps the "4m" is the height of the middle connecting piece.

Let’s calculate the area by dividing into three rectangles:

1. Left rectangle: 5m × 10m = 50 m²

2. Right rectangle: 4m × 8m = 32 m² (since 14 - 5 - 5 = 4m wide)

3. Middle rectangle: this is the part connecting them at the bottom. Its width is 5m (given), and its height is the minimum of the two sides minus the overhang?

The left side is 10m, right is 8m, so the common height at the bottom is 8m? But then the middle would be 5m × 8m, but that would overlap.

Actually, the middle part is only from the bottom up to the level where the dip starts.

From the diagram, the dip is 5m wide, and the vertical drop on the right is 4m — likely, this 4m is the height from the bottom of the shape to the top of the middle horizontal segment.

In other words, the middle horizontal segment is at a height of 4m from the bottom.

Then, the left tower is 10m tall, so from bottom to top is 10m, so the part above the middle segment on the left is 10m - 4m = 6m, but we already have the left rectangle as 5x10, which includes that.

I think I need to define the middle rectangle as the connector at the bottom.

So:

- The entire shape has a base of 14m wide and height equal to the shortest side, but it's not uniform.

Best method: consider the shape as composed of:

- A large rectangle 14m wide × 8m tall (since right side is 8m, and left is taller, but the bottom is flat)

Area = 14 × 8 = 112 m²

Then, on the left, there is an additional rectangle on top: width 5m, height = 10m - 8m = 2m → Area = 5 × 2 = 10 m²

But what about the middle dip? In this case, if I do that, I'm assuming the middle is filled up to 8m, but in reality, there is a dip in the middle.

The diagram shows that in the middle, it dips down, so my assumption is wrong.

Let's look back at the user's description: "5m" in the middle bottom, "4m" on the right inner side.

Perhaps the "4m" is the height of the right inner wall, meaning that the right tower is 8m tall, but it starts 4m above the bottom, so the bottom part is shared.

I recall that in such problems, the shape can be divided as:

- Bottom rectangle: full width 14m, height = h

- Plus left extension: 5m wide, height = 10 - h

- Plus right extension: w m wide, height = 8 - h

And the middle dip has width 5m, which should be the width between the extensions.

So, the width of the bottom rectangle is 14m.

The left extension is 5m wide, so it occupies the left 5m.

The right extension is, say, R m wide, occupying the right R m.

Then the middle part of the bottom rectangle is 14 - 5 - R m wide.

But the dip is labeled as 5m wide — probably, the width of the recessed part is 5m, which is the middle part.

So, 14 - 5 - R = 5 → 9 - R = 5 → R = 4m

So right extension is 4m wide.

Now, the height of the bottom rectangle: let's call it H.

Then, the left extension has height 10 - H

The right extension has height 8 - H

But in the diagram, there is a label "4m" on the right inner side — likely, this is the height of the right extension, so 8 - H = 4 → H = 4m

Similarly, for the left, 10 - H = 10 - 4 = 6m, but there's no label for that, but it's ok.

So, now we can calculate:

- Bottom rectangle: 14m × 4m = 56 m²

- Left top rectangle: 5m × (10 - 4)m = 5 × 6 = 30 m²

- Right top rectangle: 4m × (8 - 4)m = 4 × 4 = 16 m²

Total Area = 56 + 30 + 16 = 102 m²

Let me verify with another method.

Imagine the full rectangle 14m × 10m = 140 m²

Now, subtract the missing parts.

What is missing? On the right top, there is a rectangle that is not there: width 4m, height 10 - 8 = 2m? But also in the middle, there is a dip.

Actually, the shape has a notch in the top middle.

From the top, between x=5m to x=10m (since left 5m, then 5m dip, so from 5 to 10), the height is not 10m, but less.

Specifically, at the middle, the height is only 4m (from bottom), so from top, it's 10 - 4 = 6m down, but the dip is only in the middle 5m width.

The missing part is a rectangle in the top middle: width 5m, height = 10m - 4m = 6m? But that would be if the dip went all the way, but on the right, it's only 8m tall.

Actually, the missing area is:

- On the right: a rectangle 4m wide × (10 - 8) = 2m high → 8 m²

- In the middle: a rectangle 5m wide × (10 - 4) = 6m high? But 10 - 4 = 6, but the right side is only 8m, so at the middle, the height is 4m, so from top, it's 6m missing, but only if the left is 10m.

However, the right side is 8m, so for the middle part, from x=5 to x=10, the height is 4m, while the full height would be 10m, so missing 6m in height for that 5m width.

But on the right, from x=10 to x=14, the height is 8m, so missing 2m in height for 4m width.

So total missing area = (5m × 6m) + (4m × 2m) = 30 + 8 = 38 m²

Full rectangle 14×10=140 m²

Area = 140 - 38 = 102 m² — same as before! Perfect.

So Problem 3 is 102 m².

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Final Answers:

1. 56 m²
2. 310 cm²
3. 102 m²

Final Answer:
1. 56
2. 310
3. 102