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

Let's solve each of the three area problems step by step. These are composite shapes (made up of rectangles), so we'll break them down into simpler rectangles, find their areas, and then add or subtract as needed.

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Problem 1

Shape Description:
- A large rectangle with a "bite" taken out on the top-left.
- Total length = 15 m
- Height on the right side = 3 m
- Left side height = 5 m
- The "step" is 3 m wide at the top.

We can split this shape into two rectangles:

#### Option: Split into two rectangles

1. Bottom Rectangle:
- Width = 15 m
- Height = 3 m
- Area = 15 × 3 = 45 m²

2. Top Rectangle (on the left):
- Width = 3 m (since it's the overhang)
- Height = 5 m − 3 m = 2 m (the extra height on the left)
- Area = 3 × 2 = 6 m²

> Wait — actually, let's double-check.

Wait! The total height on the left is 5 m, but the bottom part is 3 m high, so the top rectangle is only 2 m tall (5 − 3 = 2 m). And its width is 3 m, since that's how far it extends from the left.

But wait — the total width is 15 m, and the top rectangle is only 3 m wide? That makes sense because the rest of the top is missing.

So:
- Bottom rectangle: 15 m × 3 m = 45 m²
- Top rectangle: 3 m × 2 m = 6 m²

✔ Total Area = 45 + 6 = 51 m²

Alternatively, you could think of it as:
- Full rectangle: 15 × 5 = 75 m²
- Subtract the missing piece: 12 m × 2 m = 24 m² → Wait, no.

Actually, the missing piece is on the right side?

No — let's look carefully.

The shape has:
- Left side: 5 m high
- Right side: 3 m high
- So the top part goes from left to some point, then drops down.

From the diagram:
- The horizontal line at the top starts at the left, goes 3 m across, then drops down to match the lower level.
- Then continues horizontally for 15 m.

Wait — actually, the total base is 15 m, and the top part only extends 3 m from the left, then drops down.

So:
- The left vertical segment is 5 m high.
- The bottom is 15 m long.
- The right side is only 3 m high.
- So the top of the shape is only 3 m wide at the top-left, then drops down.

So we can divide it into:
1. A vertical rectangle on the left: 3 m (width) × 5 m (height) = 15 m²
2. A horizontal rectangle on the right: 12 m (width: 15 − 3 = 12) × 3 m (height) = 36 m²

Wait — but the bottom is 15 m long, and the top is only 3 m wide? That doesn't make sense.

Let me re-read the labels.

Looking at the image:
- The total base is 15 m.
- The left side is 5 m high.
- The right side is 3 m high.
- There is a step in the middle: the top part goes out 3 m, then drops down.

So the shape is like an "L" turned sideways.

Better way:

Split into two rectangles:

1. Left rectangle: 3 m wide × 5 m high = 15 m²
2. Right rectangle: (15 − 3) = 12 m wide × 3 m high = 36 m²

Total area = 15 + 36 = 51 m²

✔ Answer: 51 m²

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Problem 2

Shape Description:
- A large rectangle with a smaller rectangle removed from the bottom-right corner.
- Dimensions:
- Overall: 10 m (top) × 9 m (left side)
- On the right side, the height is only 5 m
- The missing piece is 4 m wide (from the right edge)

So:
- The full rectangle would be 10 m × 9 m = 90 m²
- But there's a cutout on the bottom-right: 4 m wide × (9 − 5) = 4 m wide × 4 m high = 16 m²

Wait — is the cutout inside?

Actually, the figure shows:
- The top is 10 m
- The left side is 9 m
- The right side drops to 5 m, and the bottom extends inward 4 m

So it’s like a rectangle with a notch on the bottom-right.

We can split it into two parts:

#### Option 1: Two rectangles

1. Left rectangle: 6 m (10 − 4) wide × 9 m high = 54 m²
2. Right rectangle: 4 m wide × 5 m high = 20 m²

Total = 54 + 20 = 74 m²

#### Option 2: Full minus missing

- Full rectangle: 10 × 9 = 90 m²
- Missing piece: 4 m wide × (9 − 5) = 4 × 4 = 16 m²
- Area = 90 − 16 = 74 m²

✔ Answer: 74 m²

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Problem 3

Shape Description:
- A large rectangle with a rectangular hole in the center.
- Outer dimensions: 12 m (top) × 10 m (left)
- Inner cutout: 5 m wide × 6 m high

But note: the inner rectangle is not centered — it's inset from the right and top.

Let’s analyze:

- The outer shape is 12 m wide and 10 m high.
- Inside, there is a rectangular cutout of 5 m wide and 6 m high.
- This cutout is positioned such that:
- It starts from the top-right corner?
- From the diagram: the cutout is indented from the top and right.

But actually, looking at the drawing:
- The shape has a U-shape, with a rectangle missing from the center.

Wait — the cutout is inside, but it's connected to the top and right sides?

No — the shape is a big rectangle with a smaller rectangle removed from the middle.

But the labels:
- The outer width: 12 m
- Outer height: 10 m
- The inner rectangle is 5 m wide and 6 m high.

But where is it located?

From the diagram:
- The inner rectangle is placed such that it sticks out from the top and right.
- Actually, it appears to be inset from the top and right.

Wait — better approach:

Break the shape into three rectangles.

Or use subtraction method:

- Full rectangle: 12 m × 10 m = 120 m²
- Cutout: 5 m × 6 m = 30 m²
- So area = 120 − 30 = 90 m²

But is the cutout fully inside?

Yes — the inner rectangle is within the outer one, and the shape looks like a frame.

So yes, subtract the inner rectangle.

But wait — is the cutout really 5×6?

Look: the label says 5m and 6m — those are the dimensions of the cutout.

And it's placed such that it removes a rectangle from the interior.

So:
- Total area = 12 × 10 = 120 m²
- Remove 5 × 6 = 30 m²
- Final area = 120 − 30 = 90 m²

✔ Answer: 90 m²

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✔ Final Answers:

1. Area = 51 m²
2. Area = 74 m²
3. Area = 90 m²

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✔ Explanation Summary:

- For irregular shapes, break them into simple rectangles.
- Use addition if you split into parts.
- Use subtraction if you remove a piece.
- Always check dimensions carefully.

Let me know if you'd like diagrams or further explanation!