This compound shapes worksheet provides practice problems for finding the area of complex geometric figures by breaking them into simpler shapes.

Let’s solve each problem one by one. We’ll find the area of each compound shape by breaking it into simpler shapes (like rectangles, triangles, circles) and then adding or subtracting areas as needed.

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Problem 1:

Shape: Triangle with a rectangle cut out from the bottom.

- Total triangle base = 20 cm, height = 20 cm → Area = (1/2) × 20 × 20 = 200 cm²
- Rectangle inside: width = 15 cm, height = 5 cm → Area = 15 × 5 = 75 cm²
- Shaded area = Triangle - Rectangle = 200 - 75 = 125.0 cm²

✔ Final Answer for #1: 125.0

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Problem 2:

Shape: Rectangle with two circles cut out.

- Rectangle: 30 m × 43 m → Area = 30 × 43 = 1290 m²
- Each circle has diameter 10 m → radius = 5 m → Area of one circle = π × 5² ≈ 3.1416 × 25 ≈ 78.54 m²
- Two circles: 2 × 78.54 ≈ 157.08 m²
- Shaded area = Rectangle - Circles = 1290 - 157.08 ≈ 1132.9 m²

✔ Final Answer for #2: 1132.9

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Problem 3:

Shape: Circle with a right triangle cut out.

- Circle radius = 19 in → Area = π × 19² ≈ 3.1416 × 361 ≈ 1134.11 in²
- Right triangle: legs are both 19 in? Wait — look at diagram: one leg is labeled “35 in” but that can’t be if radius is 19. Actually, looking again — the triangle is drawn from center to edge, so legs should be radii? But label says “35 in” on hypotenuse? That doesn’t make sense.

Wait — re-examining: The triangle is inscribed in the circle, with right angle at center? No — actually, the triangle has vertices on the circle, and one side is diameter? Let me read labels:

It shows:
- Radius = 19 in (from center to edge)
- One side of triangle = 35 in (chord?)
- Another side = 18 in

Actually, this looks like a right triangle with legs 18 in and ? and hypotenuse 35? But 18² + x² = 35² → 324 + x² = 1225 → x² = 901 → x ≈ 30.0 — not matching radius.

Wait — perhaps the triangle is formed by two radii and a chord? But it's shaded outside the triangle? Actually, the gray area is the circle MINUS the white triangle.

Looking carefully: The triangle has sides labeled 35 in, 19 in, 18 in — but 19+18=37 > 35, so possible. But is it a right triangle? Check: 18² + 19² = 324 + 361 = 685; 35² = 1225 — not equal. So not right triangle.

But wait — there’s a right angle symbol! Yes — between the 19 in and 18 in sides. So it IS a right triangle with legs 19 in and 18 in.

So area of triangle = (1/2) × 19 × 18 = 171 in²

Circle area = π × 19² ≈ 3.1416 × 361 ≈ 1134.11 in²

Shaded area = Circle - Triangle = 1134.11 - 171 = 963.1 in²

✔ Final Answer for #3: 963.1

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Problem 4:

Shape: Rectangle with a semicircle cut out from the right side.

- Rectangle: 17 cm long, height not given? Wait — the semicircle has radius 6 cm, so diameter = 12 cm → that must be the height of the rectangle.

So rectangle: 17 cm × 12 cm → Area = 17 × 12 = 204 cm²

Semicircle: radius 6 cm → Area = (1/2) × π × 6² = (1/2) × 3.1416 × 36 ≈ 56.55 cm²

Shaded area = Rectangle - Semicircle = 204 - 56.55 ≈ 147.5 cm²

✔ Final Answer for #4: 147.5

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Problem 5:

Shape: L-shaped figure — can break into two rectangles.

Option 1: Vertical part: 8 ft tall, 4 ft wide → Area = 8 × 4 = 32 ft²
Horizontal part: extends 6 ft total, but 4 ft already counted → extra 2 ft wide, 4 ft high? Wait — better way:

Total width = 6 ft, total height = 8 ft. Cutout is 4 ft × 4 ft? Actually, the inner corner is missing.

Better: Think of full rectangle 6 ft × 8 ft = 48 ft², minus the missing square 4 ft × 4 ft = 16 ft² → 48 - 16 = 32 ft²

Alternatively: Left vertical: 8×4=32, bottom horizontal: (6-4)×4=2×4=8 → total 32+8=40? That’s wrong.

Wait — let’s draw mentally:

The shape is like a backwards L. From left: 4 ft wide, 8 ft tall. Then from bottom right, extends 2 ft more to the right (since total width 6 ft), and up 4 ft? No — the top part is only 4 ft wide.

Actually, standard way: Divide into two rectangles:

- Bottom rectangle: 6 ft wide × 4 ft high = 24 ft²
- Top rectangle: 4 ft wide × (8-4)=4 ft high = 16 ft²
- Total = 24 + 16 = 40 ft²

Yes, that matches.

✔ Final Answer for #5: 40.0

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Problem 6:

Shape: Frame — outer rectangle minus inner rectangle.

Outer: 6 ft × 2.4 ft → Area = 6 × 2.4 = 14.4 ft²

Inner: 4.4 ft × 2 ft → Area = 4.4 × 2 = 8.8 ft²

Shaded area = Outer - Inner = 14.4 - 8.8 = 5.6 ft²

✔ Final Answer for #6: 5.6

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Problem 7:

Shape: Square with a semicircle cut out from the right side.

Square: 12 m × 12 m → Area = 144 m²

Semicircle: radius = 6 m (since diameter is 12 m, same as square side) → Area = (1/2) × π × 6² ≈ (1/2) × 3.1416 × 36 ≈ 56.55 m²

Shaded area = Square - Semicircle = 144 - 56.55 ≈ 87.5 m²

✔ Final Answer for #7: 87.5

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Problem 8:

Shape: L-shaped — can divide into two rectangles.

Left part: 5 in tall × 4 in wide = 20 in²
Right part: extends 7-4=3 in wide, and height is 5-3=2 in? Wait — no.

Total width 7 in, total height 5 in. The cutout is 3 in deep on the right.

Better: Full rectangle 7×5=35 in², minus the missing rectangle 3 in × 3 in? Wait — the missing part is 3 in wide and how tall?

From diagram: the step down is 3 in, so the missing rectangle is 3 in wide and 3 in tall? But total height is 5 in, so if bottom is 3 in, top is 2 in? Confusing.

Divide:

- Bottom rectangle: 7 in wide × 3 in high = 21 in²
- Top-left rectangle: 4 in wide × (5-3)=2 in high = 8 in²
- Total = 21 + 8 = 29 in²

Check: Alternatively, left column: 5×4=20, right extension: 3×(5-3)=3×2=6 → 20+6=26? Not matching.

Wait — let’s use coordinates.

Assume bottom-left corner at (0,0). Shape goes to (7,0), up to (7,3), left to (4,3), up to (4,5), left to (0,5), down to (0,0).

So we have:

- Rectangle A: x=0 to 4, y=0 to 5 → 4×5=20
- Rectangle B: x=4 to 7, y=0 to 3 → 3×3=9
- Total = 20 + 9 = 29 in²

Yes.

✔ Final Answer for #8: 29.0

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Problem 9:

Shape: Large rectangle with a smaller rectangle cut out from the right side.

Large rectangle: 24.5 yd × 14 yd → Area = 24.5 × 14

Calculate: 24 × 14 = 336, 0.5 × 14 = 7 → total 343 yd²

Cutout rectangle: 7 yd × 7 yd? Wait — diagram shows: the cutout is 7 yd wide and 7 yd high? But the large rectangle is 14 yd tall, and the cutout starts from top? Labels say: "7 yd" for width of cutout, and "7 yd" for height? But also "14 yd" total height.

Actually, the cutout is 7 yd wide and 7 yd high, positioned at the top-right? But the shaded area includes the bottom part.

Looking: The large rectangle is 24.5 yd long, 14 yd tall. There is a rectangular hole on the right side, starting from the top, going down 7 yd, and left 7 yd.

So cutout area = 7 × 7 = 49 yd²

Shaded area = Large - Cutout = 343 - 49 = 294.0 yd²

But wait — is the cutout fully inside? Yes, since 7 < 14 and 7 < 24.5.

✔ Final Answer for #9: 294.0

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Final Answers:

1) 125.0
2) 1132.9
3) 963.1
4) 147.5
5) 40.0
6) 5.6
7) 87.5
8) 29.0
9) 294.0

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Final Answer:
1) 125.0
2) 1132.9
3) 963.1
4) 147.5
5) 40.0
6) 5.6
7) 87.5
8) 29.0
9) 294.0