Area of Compound Shapes - Free Printable

Let's solve each compound shape step by step. We'll break each shape into simpler geometric shapes (like rectangles, triangles, and trapezoids), calculate their areas, and then sum them up.

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Shape 1:

- A rectangle on the left: 4 cm × 9 cm = 36 cm²
- A right triangle on the right: base = 5 cm, height = 3 cm
Area = (1/2) × 5 × 3 = 7.5 cm²
- Total area = 36 + 7.5 = 43.5 cm²

✔ Area: 43.5 cm²

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Shape 2:

- Rectangle: 3 cm × 6 cm = 18 cm²
- Right triangle: base = 3 cm, height = 6 cm
Area = (1/2) × 3 × 6 = 9 cm²
- Total area = 18 + 9 = 27 cm²

✔ Area: 27 cm²

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Shape 3:

- Bottom rectangle: 8 cm × 6 cm = 48 cm²
- Top triangle: base = 8 cm, height = 3 cm
Area = (1/2) × 8 × 3 = 12 cm²
- But wait — the top is a triangle that’s only over part of the width? Let’s check:
The figure shows a trapezoid-like shape with a horizontal dashed line at 6 cm height and a slanted top.
Actually, it looks like:
- Lower rectangle: 8 cm × 6 cm = 48 cm²
- Upper triangle: base = 8 cm, height = 3 cm → area = (1/2)×8×3 = 12 cm²
- But the triangle is only above the rectangle?
Wait — the total height is 6 cm + 3 cm = 9 cm, but the base is 8 cm at bottom and narrows to 1 cm at the top?

Actually, let's re-analyze:

This shape has:
- A vertical side of 6 cm (bottom), then a slant going up to a point.
- From the dashed line, we see a rectangle of 8 cm × 6 cm = 48 cm²
- On top, a triangle with base 8 cm and height 3 cm → (1/2)×8×3 = 12 cm²
- But the triangle is not aligned correctly? Wait — the top is not a full triangle.

Wait! Looking again: the top is a trapezoid, or maybe a triangle on top of a rectangle?

Actually, from the diagram:
- Left side: 6 cm vertical
- Then a horizontal dashed line at 6 cm high, extending 8 cm
- Then a slanted line down to a point at 1 cm wide at the bottom?

No — the bottom is 8 cm long, and there's a 1 cm extension at the right side below the dashed line?

Wait — this shape has:
- A rectangle of 8 cm × 6 cm = 48 cm²
- A triangle on top: base = 8 cm, height = 3 cm → area = (1/2)×8×3 = 12 cm²
- But the triangle is on top, so total area = 48 + 12 = 60 cm²

But wait — the triangle is not sitting directly on top? No, the dashed line is horizontal at 6 cm, and the top goes up 3 cm more.

So yes, it's a rectangle (8×6) plus a triangle (base 8, height 3):
Total = 48 + 12 = 60 cm²

✔ Area: 60 cm²

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Shape 4:

- Top rectangle: 4 cm × 4 cm = 16 cm²
- Bottom right triangle: base = 4 cm, height = 4 cm
Area = (1/2) × 4 × 4 = 8 cm²
- Total = 16 + 8 = 24 cm²

✔ Area: 24 cm²

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Shape 5:

This is a parallelogram or can be split:
- It looks like a rectangle with two triangles on the sides?
- Or better: it’s a trapezoid with parallel sides of length 10 cm (top and bottom), and height = 4 + 3 = 7 cm?

Wait — the figure shows:
- Vertical sides: 4 cm on left, 4 cm on right, and 3 cm on bottom
- Horizontal dashed lines suggest it's composed of:
- A rectangle in the middle: 10 cm × 4 cm = 40 cm²
- But wait — the bottom extends down 3 cm, and the top is 4 cm high

Actually, this is a trapezoid with:
- Two parallel sides: one of length 10 cm (top), and the other is also 10 cm? No.

Wait — looking closely:
- The shape has:
- A horizontal segment of 10 cm at the top
- A vertical drop of 4 cm
- Then a slant down
- Then a vertical rise of 3 cm
- And back to a horizontal line

Alternatively, think of it as:
- A rectangle of 10 cm × 4 cm = 40 cm²
- Plus a right triangle on the bottom: base = 10 cm, height = 3 cm → area = (1/2)×10×3 = 15 cm²
- So total = 40 + 15 = 55 cm²

But wait — is the triangle attached to the bottom?

Yes — the bottom edge is 10 cm, and the vertical side drops 3 cm, forming a triangle.

So yes, total area = 40 + 15 = 55 cm²

✔ Area: 55 cm²

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Shape 6:

- Top rectangle: 10 cm × 4 cm = 40 cm²
- Below it, a right triangle: base = 3 cm, height = 6 cm
Area = (1/2) × 3 × 6 = 9 cm²
- But wait — the triangle is under the rectangle, and the total base is longer?

Actually:
- The shape has a rectangle on top: 10 cm × 4 cm = 40 cm²
- Below it, a triangle pointing downward, with base = 3 cm and height = 6 cm
- But the triangle is attached to the bottom-right corner?

Wait — no. The figure shows:
- A rectangle of 10 cm × 4 cm
- Then a triangle below it, with base = 3 cm and height = 6 cm, but the triangle is attached to the bottom-left?

Wait — the dashed line is horizontal at 4 cm, and then a slanted line down to a point, with a base of 3 cm.

Actually, the shape is:
- Rectangle: 10 cm × 4 cm = 40 cm²
- Triangle: base = 3 cm, height = 6 cm → area = (1/2)×3×6 = 9 cm²
- But the triangle is below the rectangle, and the total height is 4 + 6 = 10 cm?

Wait — the vertical side on the left is 4 cm (top), then 6 cm down — so total height 10 cm.

But the triangle is only on the left side, with base 3 cm and height 6 cm?

No — the triangle is under the rectangle, and the base of the triangle is 3 cm, but the rectangle is 10 cm wide.

Actually, the triangle is attached to the bottom-left, with base 3 cm and height 6 cm.

But how does it connect?

Looking carefully:
- The bottom-left corner goes down 6 cm and right 3 cm?
- So the triangle has legs 6 cm and 3 cm → area = (1/2)×6×3 = 9 cm²
- The rectangle is 10 cm × 4 cm = 40 cm²
- But the triangle is below the rectangle, and the rectangle sits on top of it?

Wait — the rectangle is on top, and the triangle is underneath, sharing the same base?

No — the rectangle is 10 cm wide, and the triangle is 3 cm wide — so they don’t align.

Wait — perhaps the triangle is to the left, under the rectangle.

Actually, the shape is:
- A rectangle of 10 cm × 4 cm = 40 cm²
- A right triangle below it, with base = 3 cm and height = 6 cm → area = 9 cm²
- But are they connected?

Yes — the rectangle sits on top of the triangle, but the triangle is only 3 cm wide, while the rectangle is 10 cm wide.

So the triangle is under the left side of the rectangle.

Thus, total area = rectangle + triangle = 40 + 9 = 49 cm²

✔ Area: 49 cm²

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Shape 7:

- Bottom rectangle: 12 cm × 4 cm = 48 cm²
- Top triangle: base = 12 cm, height = 4 cm
Area = (1/2) × 12 × 4 = 24 cm²
- Total = 48 + 24 = 72 cm²

✔ Area: 72 cm²

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Shape 8:

- Bottom rectangle: 18 cm × 8 cm = 144 cm²
- Top triangle: base = 18 cm, height = 6 cm – 8 cm? Wait — the top is shorter.

Wait — the left side is 6 cm, the right side is 8 cm, and the top is slanted.

So it’s a trapezoid with:
- Parallel sides: 6 cm and 8 cm
- Height = 18 cm (horizontal distance)
- Area = (1/2) × (6 + 8) × 18 = (1/2) × 14 × 18 = 7 × 18 = 126 cm²

Alternatively, split into:
- Rectangle: 18 cm × 6 cm = 108 cm²
- Triangle on top: base = 18 cm, height = 2 cm → (1/2)×18×2 = 18 cm²
- Total = 108 + 18 = 126 cm²

✔ Area: 126 cm²

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Shape 9:

- Left rectangle: 6 cm × 8 cm = 48 cm²
- Right triangle: base = 5 cm, height = 8 cm
Area = (1/2) × 5 × 8 = 20 cm²
- Total = 48 + 20 = 68 cm²

✔ Area: 68 cm²

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✔ Final Answers:

| Shape | Area |
|------|------|
| 1 | 43.5 cm² |
| 2 | 27 cm² |
| 3 | 60 cm² |
| 4 | 24 cm² |
| 5 | 55 cm² |
| 6 | 49 cm² |
| 7 | 72 cm² |
| 8 | 126 cm² |
| 9 | 68 cm² |

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🔍 Explanation Summary:

Each compound shape was broken into simpler parts:
- Rectangles: area = length × width
- Triangles: area = (1/2) × base × height
- Trapezoids: area = (1/2) × (sum of parallel sides) × height

We used the dashed lines (which are perpendicular) to identify heights and split the shapes appropriately.

Let me know if you'd like a visual breakdown of any specific shape!