Area Of Irregular Shapes Worksheet - Free Printable

Let’s solve each shape one by one. We’ll split each rectilinear shape into two rectangles, find the area of each rectangle (length × width), and then add them together.

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Shape 1:

We can split it vertically or horizontally. Let’s split it into:

- Left rectangle: 2cm tall and 1cm wide → Area = 2 × 1 = 2 cm²
- Right rectangle: 3cm tall and 3cm wide → Area = 3 × 3 = 9 cm²

Wait — that doesn’t match the total width. The top is labeled “3cm” for the right part, and left part has a 1cm step. So total width = 1 + 3 = 4cm? But bottom isn't labeled. Actually, looking again:

The shape has:
- Left side: 2cm height
- Top left step: 1cm wide
- Then right part: 3cm wide and 3cm high

So better to split horizontally:

Top rectangle: 3cm wide × 1cm high (since total height on right is 3cm, left is 2cm, so difference is 1cm) → Area = 3 × 1 = 3 cm²

Bottom rectangle: spans full width. What’s the full width? Left part is 1cm, right part is 3cm → total 4cm. Height is 2cm → Area = 4 × 2 = 8 cm²

Total area = 3 + 8 = 11 cm²

✔ Double-check: Another way — imagine full rectangle 4cm wide × 3cm high = 12 cm², minus the missing top-left corner which is 1cm × 1cm = 1 cm² → 12 - 1 = 11 cm². Correct!

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Shape 2:

Split into two rectangles.

Option: Split vertically.

Left rectangle: 6cm tall, 4cm wide → Area = 6 × 4 = 24 cm²

But wait — the right part sticks out only 2cm down from top? Label says: right side has 4cm vertical, then 2cm horizontal inward.

Actually, let’s read labels:

- Left side: 6cm
- Bottom: 4cm
- Right side: 4cm (top part), then 2cm going left (so indent)
- So the shape is like a big rectangle with a bite taken out of bottom right? No — actually, it's L-shaped but rotated.

Better to split into:

Top rectangle: width = ? Total bottom is 4cm, and the indent is 2cm, so top part must be 4 + 2 = 6cm wide? Wait no.

Look: The right side has two segments: 4cm down, then 2cm left. So the top rectangle is 6cm tall? No.

Actually, standard way:

Split into:

- Left rectangle: 6cm high × 4cm wide → Area = 24 cm²
- But then there’s an extra part on top right? No — the 4cm on right is shorter than left 6cm, so the difference is 2cm.

Actually, the shape is:

Imagine a rectangle 6cm high and 6cm wide? Not quite.

Labels:

- Left edge: 6cm
- Bottom edge: 4cm
- Right edge: first segment 4cm down, then 2cm left (so the inner corner)
- Top edge: not labeled, but should be 4cm + 2cm = 6cm? Because bottom is 4cm, and the indent is 2cm, so top must extend 2cm more to the right.

Yes! So:

Split into:

- Bottom rectangle: 4cm wide × 4cm high (because right side goes down 4cm before turning) → Area = 4 × 4 = 16 cm²
- Top rectangle: sits on top of the left part. Width = 6cm - 4cm = 2cm? No.

Wait — better:

The entire shape can be seen as:

A large rectangle 6cm high and 6cm wide? But bottom is only 4cm.

Actually, correct split:

Vertical split:

- Left part: 6cm high × 4cm wide → Area = 24 cm²
- Right part: only the top part, since bottom is indented. Height of right part = 6cm - 4cm = 2cm? But label says right side has 4cm then 2cm — meaning the vertical drop on right is 4cm, then horizontal 2cm left.

I think I’m overcomplicating.

Standard approach for this shape:

It’s composed of:

- A rectangle on the left: 6cm tall × 4cm wide → 24 cm²
- Plus a small rectangle on the top right: how big?

The top right part: its height is the difference between left and right sides: 6cm - 4cm = 2cm. Its width is the indent: 2cm (since bottom is 4cm, and total width must be 4cm + 2cm = 6cm? But top isn’t labeled.

Actually, from the diagram description: the right side has a 4cm vertical segment, then a 2cm horizontal segment going left. That means the top part extends 2cm beyond the bottom part.

So:

- Bottom rectangle: 4cm (width) × 4cm (height) = 16 cm²
- Top rectangle: spans full width? No.

Alternative split: horizontal.

Top rectangle: height = 6cm - 4cm = 2cm, width = 4cm + 2cm = 6cm? But we don’t know if top is 6cm.

Wait — let’s use coordinates mentally.

Assume bottom-left corner at (0,0).

Then:

- Go up 6cm to (0,6)
- Go right ? to (x,6)
- Go down 4cm to (x,2) [since right side has 4cm down]
- Go left 2cm to (x-2,2)
- Go down 2cm to (x-2,0) [to meet bottom]
- Go left to (0,0)

From bottom: from (0,0) to (4,0) because bottom is labeled 4cm.

So at y=0, x from 0 to 4.

At y=2, we have a point at (x-2,2) and also from left, at y=2, x=0 to ?

Actually, from the path:

Start at (0,0) → up to (0,6) → right to (a,6) → down to (a,2) → left to (a-2,2) → down to (a-2,0) → left to (0,0)

But bottom is from (0,0) to (4,0), so a-2 = 4 → a = 6

So:

- From (0,0) to (0,6) to (6,6) to (6,2) to (4,2) to (4,0) to (0,0)

Now split:

Rectangle 1: left part, x=0 to 4, y=0 to 6 → width 4, height 6 → area 24 cm²

Rectangle 2: right part, x=4 to 6, y=2 to 6 → width 2, height 4 → area 8 cm²

Total = 24 + 8 = 32 cm²

But wait, is that correct? The shape includes from x=4 to 6 only from y=2 to 6, yes.

Another way: full rectangle 6x6=36, minus the missing bottom-right rectangle: from x=4 to 6, y=0 to 2 → 2x2=4, so 36-4=32 cm². Yes!

But in the problem, the labels are: left 6cm, bottom 4cm, right has 4cm and 2cm. In our coordinate, right side from (6,6) to (6,2) is 4cm, then to (4,2) is 2cm left, then down to (4,0) is 2cm, but that 2cm down isn't labeled — oh, the label "2cm" is probably the horizontal indent.

In the original problem statement for shape 2: "6cm" on left, "4cm" on bottom, "4cm" on right (vertical), "2cm" on the horizontal part.

So yes, the horizontal part is 2cm, meaning the indent is 2cm.

So areas:

- Large rectangle: 6cm high × 4cm wide = 24 cm² (left part)
- Small rectangle on top right: width 2cm (the indent), height = 6cm - 4cm = 2cm? No, height should be the full height minus the lower part.

From above calculation, it's 2cm wide and 4cm high? In our coord, from y=2 to 6 is 4cm high, x=4 to 6 is 2cm wide, so 2×4=8 cm².

Total 24+8=32 cm².

But let me confirm with another split.

Split horizontally at y=4? Not necessary.

I think 32 cm² is correct.

But earlier I thought maybe different.

Let's look back at the example in the worksheet: they split into two rectangles clearly.

For shape 2, perhaps:

- Bottom rectangle: 4cm wide × 4cm high = 16 cm² (since right side drops 4cm)
- Top rectangle: spans the whole top. Width = 4cm + 2cm = 6cm? Height = 6cm - 4cm = 2cm → area = 6 × 2 = 12 cm²
- Total = 16 + 12 = 28 cm²? Contradiction.

Which is it?

In my coordinate system, when I set a=6, and bottom from 0 to 4, then at y=0, x=0 to 4; at y=2, x=4 to 6 is not filled? No.

From the path: after going down to (6,2), then left to (4,2), then down to (4,0). So the region is:

- For y from 0 to 2: x from 0 to 4
- For y from 2 to 6: x from 0 to 6

Oh! I see, I made a mistake earlier.

Correct interpretation:

The shape has:

- From y=0 to y=2: width is 4cm (from x=0 to 4)
- From y=2 to y=6: width is 6cm (from x=0 to 6)

Because:

- Start at (0,0)
- Up to (0,6)
- Right to (6,6) [assuming top is 6cm wide, though not labeled, but implied]
- Down to (6,2) [4cm down, since 6-2=4]
- Left to (4,2) [2cm left]
- Down to (4,0) [2cm down, but not labeled]
- Left to (0,0)

And bottom is labeled 4cm, which matches from x=0 to 4 at y=0.

So now, split into two rectangles:

1. Bottom rectangle: y=0 to 2, x=0 to 4 → height 2cm, width 4cm → area = 2 × 4 = 8 cm²

2. Top rectangle: y=2 to 6, x=0 to 6 → height 4cm, width 6cm → area = 4 × 6 = 24 cm²

Total = 8 + 24 = 32 cm²

Same as before.

If I split vertically:

- Left part: x=0 to 4, y=0 to 6 → 4×6=24 cm²
- Right part: x=4 to 6, y=2 to 6 → 2×4=8 cm²
- Total 32 cm²

Yes.

So area is 32 cm².

But in the label, the "2cm" is the horizontal segment, which is correct.

So for shape 2, area = 32 cm².

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Shape 3:

Labels: left side 3cm, bottom 6cm, right side 4cm, and a 2cm step on top left.

So, similar to shape 1.

Split into two rectangles.

Option: horizontal split.

The right side is 4cm, left side is 3cm, so the top part on the right is higher by 1cm.

So:

- Bottom rectangle: spans full width 6cm, height 3cm (since left is 3cm) → area = 6 × 3 = 18 cm²
- Top rectangle: on the right part. Width = ? The step is 2cm on the left, so the top rectangle starts after 2cm from left. So width = 6cm - 2cm = 4cm. Height = 4cm - 3cm = 1cm → area = 4 × 1 = 4 cm²

Total = 18 + 4 = 22 cm²

Double-check: full rectangle 6cm × 4cm = 24 cm², minus the missing top-left corner: 2cm wide × 1cm high = 2 cm² → 24 - 2 = 22 cm². Correct.

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Shape 4:

Labels: left side 5cm, bottom 10cm, right side 2cm, top 6cm.

So, it's like a big rectangle with a cut-out on the top right.

Split into two rectangles.

Option: vertical split.

- Left rectangle: 5cm high, 6cm wide (since top is 6cm) → area = 5 × 6 = 30 cm²
- Right rectangle: below the cut. Height = 2cm (given on right), width = total bottom 10cm minus left 6cm = 4cm → area = 4 × 2 = 8 cm²

Total = 30 + 8 = 38 cm²

Double-check: full rectangle 10cm × 5cm = 50 cm², minus the missing top-right rectangle: width = 10 - 6 = 4cm, height = 5 - 2 = 3cm → area = 4 × 3 = 12 cm² → 50 - 12 = 38 cm². Correct.

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Now, summarize:

1) 11 cm²
2) 32 cm²
3) 22 cm²
4) 38 cm²

Final Answer:
1) 11
2) 32
3) 22
4) 38