Math worksheet for calculating the area of compound shapes, featuring nine figures with labeled dimensions and blank spaces for answers.

Let’s solve each compound shape one by one. We’ll break them into simpler shapes (like rectangles and triangles), find their areas, then add or subtract as needed.

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Shape 1 (Top Left)
It’s a rectangle + a right triangle.
- Rectangle: width = 4 cm, height = 9 cm → Area = 4 × 9 = 36 cm²
- Triangle: base = 5 cm, height = ? The total height is 9 cm, and the rectangle takes up 3 cm of that on the right side? Wait — look again. Actually, the dashed line shows the triangle starts at 3 cm down from the top. So the triangle’s height is 9 - 3 = 6 cm.
→ Triangle area = (base × height) ÷ 2 = (5 × 6) ÷ 2 = 15 cm²
Total area = 36 + 15 = 51 cm²

Wait — let me double-check. The left side is 9 cm tall. The right side has a vertical segment of 3 cm, then the triangle goes down to the bottom. So yes, triangle height = 9 - 3 = 6 cm. Correct.

✔ Shape 1: 51 cm²

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Shape 2 (Top Middle)
Rectangle + triangle.
- Rectangle: width = 3 cm, height = 6 cm → Area = 3 × 6 = 18 cm²
- Triangle: base = 3 cm, height = 6 cm (same as rectangle) → Area = (3 × 6) ÷ 2 = 9 cm²
Total = 18 + 9 = 27 cm²

✔ Shape 2: 27 cm²

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Shape 3 (Top Right)
This looks like a trapezoid, but we can split it into a rectangle and a triangle.
Actually, better: split horizontally. There’s a rectangle at the bottom: 8 cm wide, 6 cm high → Area = 8 × 6 = 48 cm²
Above it, there’s a triangle? Wait — no, above the rectangle is a slanted part. Actually, the whole shape is a trapezoid with parallel sides 8 cm and (8+1)=9 cm? No.

Wait — look at the dashed lines. It says “dashed lines are perpendicular”. So we have:

Bottom rectangle: 8 cm × 6 cm = 48 cm²
On the right, a small triangle: base = 1 cm, height = ? The total height on the left is 6 + 3 = 9 cm. On the right, the vertical drop is only 6 cm? Wait — the diagram shows:

Left side: 6 cm (bottom) + 3 cm (top) = 9 cm total height.
Right side: only 6 cm high? And then a斜边 going up to meet the top left.

Actually, the shape is made of:
- A rectangle: 8 cm wide × 6 cm high = 48 cm²
- A triangle on top: base = 8 cm, height = 3 cm? But wait — the top edge is slanted. Actually, the dashed line is horizontal at 6 cm height. Above that, from left to right, it goes from 3 cm above the dashed line down to... actually, the right side doesn’t go up — it stops at 6 cm. So above the rectangle, we have a triangle that spans the full 8 cm width? No.

Wait — re-examining: The left side is 9 cm total (6 + 3). The right side is only 6 cm. The top connects them with a straight line. So this is a trapezoid with parallel sides: left = 9 cm, right = 6 cm, and distance between them (width) = 8 cm? But also there’s an extra 1 cm on the bottom right.

Actually, looking closely: the bottom is 8 cm + 1 cm = 9 cm total? No — the label says "8 cm" for the main bottom, and "1 cm" sticking out on the right. So the shape is:

- A rectangle: 8 cm × 6 cm = 48 cm²
- A triangle on the right: base = 1 cm, height = 6 cm? But that would be if it were vertical. Actually, the rightmost part is a triangle with base 1 cm and height equal to the difference in heights? This is confusing.

Alternative approach: Split vertically.

From left to right:
- First 8 cm: it's a trapezoid with left height 9 cm, right height 6 cm → average height = (9+6)/2 = 7.5 cm → area = 8 × 7.5 = 60 cm²? But that ignores the extra 1 cm.

Wait — the diagram shows:

The bottom is labeled "8 cm" under the main part, and "1 cm" under the little extension on the right. The left side is 6 cm (lower) + 3 cm (upper) = 9 cm. The right side of the main part is 6 cm, and then there's a斜边 going down to the end of the 1 cm extension.

So perhaps:

Main part (left 8 cm): rectangle 8×6 = 48 cm² plus a triangle on top: base 8 cm, height 3 cm → area = (8×3)/2 = 12 cm² → subtotal 60 cm²

Then the extra 1 cm on the right: it’s a triangle with base 1 cm and height 6 cm? But that would be attached to the bottom. Actually, since the right side drops from 6 cm to 0 over 1 cm, it’s a right triangle with legs 1 cm and 6 cm → area = (1×6)/2 = 3 cm²

But wait — is that correct? If the main part ends at 6 cm height, and then we extend 1 cm to the right and go down to ground level, yes, that’s a triangle.

So total area = 48 (rectangle) + 12 (top triangle) + 3 (right triangle) = 63 cm²

But let me verify another way.

Think of the whole shape as a large rectangle minus something? Not easy.

Or use coordinates. Place bottom-left corner at (0,0).

Then points:
- (0,0)
- (8,0)
- (9,0) [since 8+1]
- (9, ?) — no, the right side goes up to where? The diagram shows the rightmost point is at x=9, y=0? And the top-right of the main part is at (8,6)? Then the top-left is at (0,9). And there’s a line from (0,9) to (8,6), and from (8,6) to (9,0)? That makes sense.

So we can split into two parts:

Part 1: polygon from (0,0) to (8,0) to (8,6) to (0,9) back to (0,0). This is a trapezoid.

Area of trapezoid = (sum of parallel sides) × height / 2. Here, the two parallel sides are vertical? Better to use shoelace formula or split.

Split into rectangle and triangle:

From (0,0) to (8,0) to (8,6) to (0,6) to (0,0): rectangle 8×6=48

Plus triangle from (0,6) to (0,9) to (8,6): base 8, height 3 → area 12

Subtotal: 60

Now part 2: triangle from (8,6) to (9,0) to (8,0). Base along x from 8 to 9 is 1 cm, height from y=0 to y=6 is 6 cm, but it’s a right triangle with legs 1 and 6 → area = (1×6)/2 = 3

Total: 60 + 3 = 63 cm²

Yes.

✔ Shape 3: 63 cm²

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Shape 4 (Middle Left)
Looks like a square on top and a triangle below.

Top: square 4 cm × 4 cm = 16 cm²

Bottom: triangle with base 4 cm, height 4 cm → area = (4×4)/2 = 8 cm²

Total = 16 + 8 = 24 cm²

✔ Shape 4: 24 cm²

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Shape 5 (Middle Center)
This is a bit tricky. Dashed lines show it’s divided into three parts? Or two?

Actually, it seems like a central rectangle with triangles on top and bottom.

Central rectangle: width 10 cm, height 4 cm → area = 10 × 4 = 40 cm²

Top triangle: base 10 cm, height 4 cm → area = (10×4)/2 = 20 cm²

Bottom triangle: base 10 cm, height 3 cm → area = (10×3)/2 = 15 cm²

Total = 40 + 20 + 15 = 75 cm²

Is that correct? Let me see the diagram: left side has 4 cm (top triangle height), then 10 cm width, then 4 cm (middle rectangle height?), then 3 cm (bottom triangle height). Yes, so total height on left is 4+4+3=11 cm, which matches.

✔ Shape 5: 75 cm²

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Shape 6 (Middle Right)
This is an L-shape or something. Can be seen as a big rectangle minus a smaller rectangle, or as two rectangles.

Option 1: Big rectangle 10 cm × (4+6)=10 cm? Height is 4+6=10 cm, width 10 cm → area 100 cm², but there’s a cut-out.

Actually, the shape is:

Top rectangle: 10 cm wide × 4 cm high = 40 cm²

Bottom part: it’s a rectangle 7 cm wide? Because the right side has a 3 cm indentation. Total width 10 cm, minus 3 cm on the right, so 7 cm wide, and 6 cm high → area = 7 × 6 = 42 cm²

Total = 40 + 42 = 82 cm²

Check: the bottom-left corner to bottom-right of the lower part is 10 - 3 = 7 cm, yes.

✔ Shape 6: 82 cm²

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Shape 7 (Bottom Left)
Trapezoid? Or rectangle + triangle.

Bottom rectangle: 12 cm × 4 cm = 48 cm²

Top triangle: base 12 cm, height 4 cm → area = (12×4)/2 = 24 cm²

Total = 48 + 24 = 72 cm²

The left side is 4 cm (rectangle) + nothing? Wait, the left side is labeled 4 cm for the rectangle, and the triangle sits on top, so total height on left is 4 cm (rect) + 4 cm (triangle height) = 8 cm, but the right side is only 4 cm? No — in the diagram, the right side of the triangle is vertical? Actually, looking: the shape has a rectangle at bottom 12x4, and on top, a triangle that covers the whole 12 cm width, with height 4 cm, so the apex is centered? But the diagram shows the right side of the triangle is vertical? No — it’s a right triangle? Wait, no.

Actually, the dashed line is horizontal at 4 cm height. Below it: rectangle 12x4. Above it: a triangle with base 12 cm and height 4 cm, but is it symmetric? The diagram doesn't specify, but since it's a compound shape and dashed lines are perpendicular, likely the triangle is sitting on top with its base the full 12 cm, and height 4 cm, so area 24 cm².

Yes.

✔ Shape 7: 72 cm²

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Shape 8 (Bottom Middle)
Similar to previous. Bottom rectangle: 18 cm × 8 cm = 144 cm²

Top triangle: base 18 cm, height 6 cm → area = (18×6)/2 = 54 cm²

Total = 144 + 54 = 198 cm²

Left side: 8 cm (rect) + 6 cm (triangle) = 14 cm, right side is 8 cm, so the triangle slopes down to the right? But in the diagram, the top is slanted, and the right side is vertical 8 cm, left side is 8+6=14 cm. So yes, the triangle has height 6 cm over the full 18 cm base.

✔ Shape 8: 198 cm²

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Shape 9 (Bottom Right)
This is a rectangle plus a triangle.

Left part: rectangle 6 cm wide × 8 cm high = 48 cm²

Right part: triangle with base 5 cm, height 8 cm → area = (5×8)/2 = 20 cm²

Total = 48 + 20 = 68 cm²

The dashed line is vertical at 6 cm from left, so the rectangle is 6x8, and the triangle is attached to the right, base 5 cm, same height 8 cm.

✔ Shape 9: 68 cm²

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Now, compiling all answers:

1. 51 cm²
2. 27 cm²
3. 63 cm²
4. 24 cm²
5. 75 cm²
6. 82 cm²
7. 72 cm²
8. 198 cm²
9. 68 cm²

Final Answer:
51, 27, 63, 24, 75, 82, 72, 198, 68