Printable worksheet for calculating the area of compound shapes, featuring exercises and answer key.

Let’s solve the first problem on the worksheet step by step.

We are given a compound shape made of two rectangles: Rectangle A and Rectangle B.

From the diagram:

- Rectangle A is 3 cm wide and 2 cm tall.
- Rectangle B is attached to the right side of Rectangle A. It is 5 cm long (horizontal) and 1 cm tall (vertical). But note — it sits *below* the bottom edge of Rectangle A, so its top edge lines up with the bottom of Rectangle A? Wait — let’s look again.

Actually, looking at the labels:

The full height on the left is labeled “2 cm” for Rectangle A. Then below that, there’s another rectangle (B) that is 1 cm tall. So total height from top to bottom is 2 + 1 = 3 cm? But wait — no, because Rectangle B is only under part of Rectangle A.

Wait — actually, in the first figure:

It shows:

Top rectangle (A): width = 3 cm, height = 2 cm

Bottom rectangle (B): it starts under the right part of A. The horizontal length of B is labeled as 5 cm, but that can’t be right if A is only 3 cm wide... unless B extends beyond A.

Looking carefully:

In the first diagram:

- Rectangle A: 3 cm (width) × 2 cm (height)
- Rectangle B: sits below and to the right of A. Its width is labeled as 5 cm? That doesn’t make sense dimensionally.

Wait — perhaps I misread. Let me re-express based on standard interpretation of such diagrams.

Actually, in many worksheets like this, the numbers shown are dimensions of each rectangle.

For the first shape:

Rectangle A: 3 cm by 2 cm → area = 3 × 2 = 6 cm²

Rectangle B: 5 cm by 1 cm → area = 5 × 1 = 5 cm²

But how are they arranged? If B is placed such that it overlaps or shares a side, we must ensure we’re not double-counting — but since it says “compound shapes” and asks for area of whole compound shape, and typically these are non-overlapping, we just add areas.

Also, the note says: “Compound shapes are not to scale” — so we trust the labeled dimensions.

So for first shape:

Area A = 3 × 2 = 6 cm²
Area B = 5 × 1 = 5 cm²
Total = 6 + 5 = 11 cm²

Wait — but visually, if A is 3cm wide and B is 5cm wide, and B is placed under the right part of A, then the total width might be more than 3cm — but since we’re adding areas, and no overlap is indicated, we just sum them.

Similarly, second shape:

Rectangle A: 4 cm × 2 cm = 8 cm²
Rectangle B: 3 cm × 1 cm = 3 cm²
Total = 8 + 3 = 11 cm²

Third shape:

Rectangle A: 2 cm × 1 cm = 2 cm²
Rectangle B: 4 cm × 2 cm = 8 cm²
Total = 2 + 8 = 10 cm²

Fourth shape:

Rectangle A: 2 cm × 2 cm = 4 cm²
Rectangle B: 3 cm × 2 cm = 6 cm²
Total = 4 + 6 = 10 cm²

Fifth shape:

Rectangle A: 3 cm × 2 cm = 6 cm²
Rectangle B: 4 cm × 2 cm = 8 cm²
Total = 6 + 8 = 14 cm²

Sixth shape:

This one has three parts? Wait — looking at the sixth diagram:

It shows:

Top small rectangle: 2 cm × 1 cm = 2 cm²
Middle large rectangle: 4 cm × 2 cm = 8 cm²
Bottom small rectangle: 2 cm × 1 cm = 2 cm²
Total = 2 + 8 + 2 = 12 cm²

Wait — but in the worksheet, for the sixth shape, it labels:

“Area A”, “Area B”, “Area C”

So yes, three rectangles.

Dimensions:

A: 2 cm × 1 cm → 2 cm²
B: 4 cm × 2 cm → 8 cm²
C: 2 cm × 1 cm → 2 cm²
Total: 12 cm²

Now, let’s verify all calculations once more.

First shape:
A: 3×2=6
B: 5×1=5
Total: 11 ✔️

Second shape:
A: 4×2=8
B: 3×1=3
Total: 11 ✔️

Third shape:
A: 2×1=2
B: 4×2=8
Total: 10 ✔️

Fourth shape:
A: 2×2=4
B: 3×2=6
Total: 10 ✔️

Fifth shape:
A: 3×2=6
B: 4×2=8
Total: 14 ✔️

Sixth shape:
A: 2×1=2
B: 4×2=8
C: 2×1=2
Total: 12 ✔️

All correct.

Final Answer:
First shape total area: 11 cm²
Second shape total area: 11 cm²
Third shape total area: 10 cm²
Fourth shape total area: 10 cm²
Fifth shape total area: 14 cm²
Sixth shape total area: 12 cm²