Practice calculating the area of complex shapes with this Grade 6 worksheet featuring L-shaped and U-shaped figures.

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 width is 12m, and the right horizontal part is 8m long → so left part width = 12m - 8m = 4m
Area of Rectangle A = 8m × 4m = 32 m²

- Rectangle B (bottom horizontal part):
Length = 8m, Height = 3m
Area of Rectangle B = 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 x 5m) = 40 m² → 96 - 40 = 56 m². 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 width = 18cm, right small part is 5cm → left part width = 18cm - 5cm = 13cm
But wait — actually, looking at the diagram: the right side has a “step” that goes down 10cm and over 5cm. So better to split as:

Actually, let’s do this clearly:

Split vertically:

- Left rectangle: height = 20cm, width = 18cm - 5cm = 13cm → Area = 20 × 13 = 260 cm²
- Right rectangle: height = 20cm - 10cm = 10cm, width = 5cm → Area = 10 × 5 = 50 cm²

Wait — no! 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, go down 10cm, then right 5cm? Actually, label says “10cm” on the vertical drop, and “5cm” on the horizontal part.

Better approach: Split horizontally.

Top rectangle: width = 18cm - 5cm = 13cm, height = 10cm → Area = 13 × 10 = 130 cm²

Bottom rectangle: full width 18cm, height = 20cm - 10cm = 10cm → Area = 18 × 10 = 180 cm²

Total = 130 + 180 = 310 cm²

✔ Check another way: Full rectangle 18x20 = 360 cm², minus missing top-right rectangle: 5cm x 10cm = 50 cm² → 360 - 50 = 310 cm². Correct!

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Problem 3:

This one looks like a U-shape or a rectangle with a bite taken out of the top middle.

We can think of it as a big rectangle minus a smaller rectangle in the middle top.

Big rectangle: width = 14m, height = 10m → Area = 14 × 10 = 140 m²

Now, what’s missing? In the top middle, there’s a rectangular cutout.

From diagram:
- The cutout starts after 5m from left, ends before 5m from right? Wait, labels:

Left side: 5m (top left flat), then drops down 4m? Wait, let's read carefully.

Actually, the shape has:

- Left column: 10m tall, 5m wide
- Right column: 8m tall, ? wide — but total bottom is 14m, left is 5m, middle gap is 5m? Wait, diagram shows:

Top view: from left, 5m across, then down 4m, then 5m across (the dip), then up 4m? No — label says “4m” next to the vertical drop inside.

Actually, better to split into three parts:

- Left rectangle: 5m wide × 10m high = 50 m²
- Right rectangle: how wide? Total bottom 14m, left 5m, middle dip 5m → right = 14 - 5 - 5 = 4m? But diagram says right side is 8m tall.

Wait — perhaps:

The shape is made of:

- Bottom rectangle: 14m wide × 8m high = 112 m²
- Plus two top rectangles on sides:
- Left top: 5m wide × (10m - 8m) = 5m × 2m = 10 m²
- Right top: ? wide × 2m — but right side total height is 8m, same as bottom? Wait, diagram says right side is labeled 8m, left is 10m.

Actually, looking again:

The figure has:

- Left side: 10m tall
- Right side: 8m tall
- Bottom: 14m
- Top left: 5m across
- Then dips down 4m? Label says “4m” next to the inner vertical edge.
- Then across 5m (labeled “5m”)
- Then up to meet right side.

So, we can split into:

1. Left rectangle: 5m (width) × 10m (height) = 50 m²
2. Middle bottom rectangle: 5m (width) × (10m - 4m)? Wait, no.

Alternative: Think of the whole thing as a big rectangle 14m x 10m = 140 m², then subtract the missing part in the top middle.

What’s missing? A rectangle that is 5m wide (the dip) and how tall? From the top, it dips down 4m? But left side is 10m, right side is 8m — inconsistency?

Wait — perhaps the “4m” is the depth of the dip from the top.

Assume:

- The top surface has a notch: from left, 5m flat, then down 4m, then 5m across (so the notch is 5m wide and 4m deep), then up to the right side which is only 8m tall? That doesn't make sense because if left is 10m and you go down 4m, you're at 6m, but right is 8m — mismatch.

I think I misread. Let me interpret based on standard such problems.

Common interpretation for Problem 3:

It’s a rectangle 14m wide and 10m tall, but with a rectangular piece removed from the top center.

The removed piece is 5m wide (as labeled "5m" in the dip) and 4m tall (as labeled "4m" for the vertical drop).

But then the right side should be 10m - 4m = 6m? But diagram says 8m. Contradiction.

Wait — look at the labels again:

In Problem 3 diagram:

- Left side: 10m
- Bottom: 14m
- Top left segment: 5m
- Then a vertical drop labeled "4m"
- Then a horizontal segment labeled "5m"
- Then a vertical rise? Not labeled, but then right side is labeled "8m"

Ah! So the right side is 8m tall, meaning from bottom to top on right is 8m.

So the shape is not symmetric.

Let’s define coordinates or just split into rectangles.

Split into three vertical strips:

- Left strip: width 5m, height 10m → Area = 5 × 10 = 50 m²
- Middle strip: width 5m, but height? From bottom to where? The dip goes down 4m from the top, but top on left is 10m, so at middle, the height is 10m - 4m = 6m? But then right side is 8m — still inconsistent.

Perhaps the "4m" is the height of the protrusion or something else.

Another idea: The shape consists of:

- A base rectangle: 14m wide × 8m high = 112 m² (since right side is 8m, and bottom is flat)
- Plus a left extension on top: from y=8m to y=10m, width 5m → Area = 5m × 2m = 10 m²
- Minus the dip in the middle? But the dip is already accounted for if we consider the base is only 8m high.

Wait, the dip is in the top part. After the left 5m, it goes down 4m — but if the base is 8m, and left goes up to 10m, then from x=5m to x=10m (since 5m dip), the height is 10m - 4m = 6m? But then from x=10m to x=14m, it should be 8m, but 6m ≠ 8m.

I think there's a mistake in my reading. Let me assume the "4m" is the depth of the indentation from the top level.

Standard solution for such problems:

For Problem 3, common approach:

Area = area of large rectangle minus area of the cut-out rectangle.

Large rectangle: 14m × 10m = 140 m²

Cut-out rectangle: width = 5m (given), height = 4m (given) → Area = 5 × 4 = 20 m²

But then the right side would be 10m, but diagram says 8m — contradiction.

Unless the 8m is a typo or I'm misseeing.

Looking back at user's image description: in Problem 3, it says "8m" on the right side, "10m" on left, "14m" bottom, "5m" top left, "5m" in the dip, "4m" vertical in the dip.

Perhaps the 8m is the height of the right part, and the left is 10m, so the difference is 2m, and the dip is 4m down from left top, so from left top at 10m, down 4m to 6m, but right is at 8m — still not matching.

Another possibility: the "4m" is not the depth, but the height of the right part of the dip or something.

Let's calculate by dividing into parts:

- Rectangle 1: left part, 5m wide × 10m high = 50 m²
- Rectangle 2: right part, how wide? Total 14m, left 5m, middle 5m, so right = 4m? But diagram doesn't specify, but from context, likely right width is 14 - 5 - 5 = 4m, and height 8m → Area = 4 × 8 = 32 m²
- Rectangle 3: middle bottom part, between left and right, width 5m, height? Since left is 10m, right is 8m, and there's a dip of 4m, perhaps the middle part has height min(10,8) = 8m? But then the dip is additional.

I recall that in some worksheets, for Problem 3, the intended solution is:

Think of it as a rectangle 14m x 8m = 112 m² for the bottom part.

Then on top, on the left, a rectangle 5m x 2m = 10 m² (since 10m - 8m = 2m extra height on left).

On the right, no extra since it's 8m.

But in the middle, there is a dip: from x=5m to x=10m, instead of being at 10m or 8m, it's lower by 4m from the left top, so from y=10m down to y=6m, but the base is at y=0, so height in middle is 6m? But then it's not connected properly.

Perhaps the "4m" is the amount it dips below the left top, but the right top is at 8m, so the dip is from 10m down to 6m, but the right is at 8m, so between x=10m to x=14m, it rises from 6m to 8m? That would be a slope, but the shape is rectilinear.

I think there might be a mislabeling, but in many similar problems, for this exact worksheet, the answer is calculated as:

Area = (14 * 8) + (5 * 2) - (5 * 4) ? Let's see.

14*8 = 112 (base)
+5*2 = 10 (left top extension)
-5*4 = -20 (the dip) -> 112+10-20 = 102 m²

But why subtract 20? If the dip is 5m wide and 4m deep, and it's cutting into the left extension.

Let's visualize:

- From x=0 to 5m: height 10m
- From x=5m to 10m: height 10m - 4m = 6m (because it dips down 4m)
- From x=10m to 14m: height 8m

Then areas:

- Left: 5 * 10 = 50
- Middle: 5 * 6 = 30
- Right: 4 * 8 = 32 (since 14-5-5=4m wide)

Total = 50 + 30 + 32 = 112 m²

But is the right width 4m? 14 - 5 - 5 = 4, yes.

And heights: left 10m, middle 6m (10-4), right 8m.

But is the middle height really 6m? The dip is labeled "4m", which is likely the vertical drop from the left top, so yes.

And the right side is given as 8m, which matches.

So Area = 5*10 + 5*6 + 4*8 = 50 + 30 + 32 = 112 m²

But let's verify with another method.

Imagine the shape as a large rectangle 14m x 10m = 140 m²

Minus the parts that are missing:

- In the middle top, from x=5 to 10, y=6 to 10: a rectangle 5m x 4m = 20 m² missing? But at x=10 to 14, it's only 8m high, so from y=8 to 10, it's also missing.

Actually, the missing parts are:

- From x=5 to 10, y=6 to 10: 5x4 = 20 m²
- From x=10 to 14, y=8 to 10: 4x2 = 8 m² (since width 4m, height 2m)

Total missing = 20 + 8 = 28 m²

Large rectangle 14*10 = 140

Area = 140 - 28 = 112 m²

Same as before.

In the first method, we have left 50, middle 30, right 32, sum 112.

So it's consistent.

Therefore, for Problem 3, area is 112 m².

But in the diagram, the "4m" is labeled on the vertical drop in the middle, which is from y=10 to y=6, so 4m, correct.

And right side is 8m, so from y=0 to 8.

Yes.

So final answers:

1. 56 m²

2. 310 cm²

3. 112 m²

Now, to box the final answer as per instruction.

Final Answer:
1. 56 m²
2. 310 cm²
3. 112 m²