Find the area of irregular shapes in this Grade 6 math worksheet.

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

---

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 = 12 - 8 = 4m
Area = 8 × 4 = 32 m²

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

Total Area = 32 + 24 = 56 m²

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

---

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 of 10cm. So actually, we can split horizontally or vertically.

Better to split vertically:

- Left rectangle: height = 20cm, width = 18 - 5 = 13cm? Wait — no, let’s read labels again.

Actually, from the diagram:

Top right part sticks out 5cm wide and 10cm tall.

So better to split as:

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

- Top rectangle: only on the left, width = 18 - 5 = 13cm? Wait — no.

Wait — label says “10cm” is the height of the step down, and “5cm” is the width of the protruding part on the right.

Actually, the shape is like a big rectangle with a smaller rectangle attached on top right? No — looking again:

It’s a large rectangle 20cm tall and 18cm wide, but the top right corner is cut off? No — actually, it’s built as:

Left part: 20cm tall, and right part is shorter.

Standard way: split into two rectangles:

Option 1: Vertical split

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

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

Total = 260 + 50 = 310 cm²

But wait — that doesn’t match the diagram labeling. Let me re-read.

Diagram shows:

- Left side labeled 20cm (full height)

- Bottom labeled 18cm (full width)

- On the right, there’s a step: from top, down 10cm, then right 5cm? Actually, the 10cm is the height of the upper right block, and 5cm is its width.

Actually, the shape is:

A big rectangle 18cm wide and 20cm tall, minus a rectangle in the top right that is 5cm wide and 10cm tall? No — because if you remove that, the remaining height on the right would be 10cm, which matches.

Wait — let’s think differently.

From the diagram:

The entire shape can be seen as:

- A bottom rectangle: 18cm wide × (20 - 10) = 10cm high → 18 × 10 = 180 cm²

- Plus a top-left rectangle: width = 18 - 5 = 13cm, height = 10cm → 13 × 10 = 130 cm²

Total = 180 + 130 = 310 cm²

Same as before.

Alternatively, full rectangle 18×20=360, minus the missing top-right rectangle: 5cm wide × 10cm high = 50 → 360 - 50 = 310 cm². Yes!

So Area = 310 cm²

---

Problem 3:

This one is trickier — it’s like a U-shape or a rectangle with a bite taken out of the top middle.

We can calculate the area of the full outer rectangle and subtract the missing middle part.

Outer rectangle:

Width = 14m, Height = 10m → Area = 14 × 10 = 140 m²

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

From the diagram:

- The notch is 5m wide (labeled "5m" inside the notch)

- And 4m deep? Wait — labeled "4m" next to the notch depth.

Also, the sides: left side is 10m, right side is 8m — that suggests the notch goes down 2m from the top? Because 10 - 8 = 2m? But labeled 4m?

Wait — let’s read carefully.

Labels:

- Left side: 10m (full height)

- Right side: 8m — so the right side is shorter? That means the shape is not symmetric.

Actually, looking at the diagram:

It’s a rectangle with a rectangular indentation on the top.

Bottom width: 14m

Left height: 10m

Right height: 8m

In the middle top, there’s a dip: labeled 5m (width of dip), and 4m (depth of dip?).

But if left is 10m and right is 8m, and there’s a dip of 4m, that might not add up.

Alternative approach: split into three rectangles.

Left rectangle: width = 5m (labeled on top left), height = 10m → Area = 5 × 10 = 50 m²

Right rectangle: width = ? Total width 14m, left is 5m, middle dip is 5m, so right should be 14 - 5 - 5 = 4m? But labeled 8m height.

Height of right part is 8m, so area = 4 × 8 = 32 m²

Middle part: between left and right, but it’s indented. The dip is 5m wide and how deep? From the top, it goes down 4m? But left is 10m, right is 8m — inconsistency?

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

Assume the top of the left and right parts are at different heights? That complicates.

Another way: the shape can be seen as a large rectangle minus a smaller rectangle in the middle top.

Large rectangle: 14m wide × 10m high = 140 m²

Missing part: a rectangle in the top middle. Its width is 5m (given). What is its height?

From the diagram, the dip goes down 4m from the top? But the right side is only 8m high, while left is 10m — so the top is not flat.

Perhaps the 4m is the vertical drop of the dip.

Let’s use coordinates or careful reading.

Notice: the bottom is 14m.

Top has three segments: left 5m, then a gap (the dip), then right part.

The dip is labeled 5m wide and 4m deep — meaning from the top edge, it goes down 4m.

But the left column is 10m tall, so if the dip starts at the top and goes down 4m, then the base of the dip is at 10 - 4 = 6m from bottom? But the right side is only 8m tall — contradiction.

Unless the right side's 8m is from bottom to its top, and the left is 10m, so the top is slanted? But that seems unlikely for this level.

Perhaps I misread the diagram.

Looking back at user's image description:

For problem 3:

- Left side: 10m

- Bottom: 14m

- Top left segment: 5m

- Then a dip: labeled 5m (horizontal) and 4m (vertical)

- Then right side: 8m

Ah — probably, the 4m is the depth of the dip, and the right side being 8m means that from the bottom to the top of the right part is 8m, while left is 10m, so the dip must account for the difference.

Actually, the total height on left is 10m, on right is 8m, and the dip is in the middle.

The dip has a vertical side of 4m — likely, that 4m is the difference in height between left and the dip floor or something.

Best to split into three parts:

1. Left rectangle: width 5m, height 10m → area = 50 m²

2. Right rectangle: width = ? Total width 14m, left 5m, dip 5m, so right width = 14 - 5 - 5 = 4m, height 8m → area = 4 × 8 = 32 m²

3. Middle bottom part: under the dip. The dip is 5m wide, and how tall? From the bottom to the start of the dip.

Since left is 10m and the dip goes down 4m from the top, but the top of left is higher than right.

Actually, the dip's vertical label "4m" is probably the height of the dip wall, meaning from the top of the dip to the top of the adjacent parts.

But since left is 10m and right is 8m, perhaps the dip is measured from the lower side.

To avoid confusion, let's calculate the area as the sum of the left part, the right part, and the connecting bottom part.

The bottom part spans the full 14m width, but its height is limited by the shortest side, which is 8m? But left is taller.

Actually, the shape has a constant bottom, and the top varies.

The minimum height is 8m (on the right), and on the left it extends up to 10m, and in the middle there's a dip of 4m down from the top.

Perhaps the 4m is the depth from the highest point.

Assume the highest point is the left top at 10m.

Then the dip goes down 4m, so the floor of the dip is at 10 - 4 = 6m from bottom.

But the right side is only 8m high, which is above 6m, so that works.

Then, the middle section under the dip: from x=5m to x=10m (since dip is 5m wide), and from y=0 to y=6m? But the right part is only up to 8m, so from y=6m to y=8m, is there material?

This is messy.

Another standard way for such problems: the area is the area of the bounding box minus the missing parts.

Bounding box: 14m wide × 10m high = 140 m²

Missing parts:

- In the top middle, a rectangle of 5m wide and 4m high (the dip) — but is that correct? If we remove a 5x4 rectangle from the top middle, then the remaining height on the right would be 10m, but the diagram says right side is 8m, so that doesn't match.

Unless the 8m is a mistake, or I'm misinterpreting.

Let's look at the labels again as per user's text:

"3.
5m
10m
5m
4m
8m
14m"

And the shape is described as having a dip in the top middle.

Perhaps the 4m is not the depth of the dip, but the height of the right part's extension or something.

I recall that in some worksheets, for such a shape, you can calculate as:

Area = area of left rectangle + area of right rectangle + area of the bottom connector.

Left: 5m * 10m = 50 m²

Right: let's say width w, height 8m. What is w? Total width 14m, left 5m, dip 5m, so right width = 14 - 5 - 5 = 4m, so 4*8=32 m²

Now, the middle part: between left and right, from x=5 to x=10, but from y=0 to y= min(10,8) = 8m? But the dip is there.

The dip is 5m wide and 4m deep — if "deep" means how much it is indented from the top, and since the left is 10m, the dip floor is at 10-4=6m, but the right is only 8m, so from y=6m to y=8m, in the middle, is there material? Probably not, because the dip is only in the top.

Perhaps the shape is:

- From x=0 to 5: y=0 to 10

- From x=5 to 10: y=0 to 6 (because dip of 4m from top, so 10-4=6)

- From x=10 to 14: y=0 to 8

Then area = (5*10) + (5*6) + (4*8) = 50 + 30 + 32 = 112 m²

Let me verify with another method.

Full rectangle 14*10=140

Minus the missing parts:

- In the top middle, from x=5 to 10, y=6 to 10: that's 5m * 4m = 20 m² missing

- Also, on the right, from x=10 to 14, y=8 to 10: that's 4m * 2m = 8 m² missing

Total missing = 20 + 8 = 28 m²

Area = 140 - 28 = 112 m²

Yes! Matches.

So Area = 112 m²

---

Final Answers:

1. 56 m²
2. 310 cm²
3. 112 m²

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