Geometry Worksheets | Area Worksheets - Free Printable

Let's solve each compound shape step by step. We'll break down each figure into simpler shapes (like rectangles, triangles, and circles), calculate their areas, and then add or subtract as needed.

---

1) Trapezoid

- Bases: 14 in and 7 in
- Height: 14 in

Area of a trapezoid = $\frac{1}{2} \times (b_1 + b_2) \times h$

$$
= \frac{1}{2} \times (14 + 7) \times 14 = \frac{1}{2} \times 21 \times 14 = 10.5 \times 14 = 147 \text{ in}^2
$$

✔ Area: 147.0 in²

---

2) Rectangle with a semicircle on top

- Rectangle: 18 cm × 18 cm
- Semicircle: diameter = 18 cm → radius = 9 cm

Rectangle area = $18 \times 18 = 324$ cm²
Semicircle area = $\frac{1}{2} \pi r^2 = \frac{1}{2} \pi (9)^2 = \frac{1}{2} \pi \times 81 = 40.5\pi \approx 127.2$ cm²

Total area = $324 + 127.2 = 451.2$ cm²

✔ Area: 451.2 cm²

---

3) Rectangle with a semicircle on top

- Rectangle: 20 yd × 15 yd
- Semicircle: diameter = 6 yd → radius = 3 yd

Rectangle area = $20 \times 15 = 300$ yd²
Semicircle area = $\frac{1}{2} \pi (3)^2 = \frac{1}{2} \pi \times 9 = 4.5\pi \approx 14.1$ yd²

Total area = $300 + 14.1 = 314.1$ yd²

✔ Area: 314.1 yd²

---

4) Triangle on top of a semicircle

- Triangle: base = 8 m, height = 12 m
- Semicircle: diameter = 8 m → radius = 4 m

Triangle area = $\frac{1}{2} \times 8 \times 12 = 48$ m²
Semicircle area = $\frac{1}{2} \pi (4)^2 = \frac{1}{2} \pi \times 16 = 8\pi \approx 25.1$ m²

Total area = $48 + 25.1 = 73.1$ m²

✔ Area: 73.1 m²

---

5) L-shaped figure

Break into two rectangles:

- Top rectangle: 12 in × 12 in = 144 in²
- Bottom rectangle: 20 in × 12 in = 240 in²

But wait — the top rectangle is only 12 in wide, and the bottom is 20 in wide. The overlapping part is 12 in × 12 in.

Actually, better to split it:
- Left side: 12 in (height) × 12 in (width) = 144 in²
- Right side: 12 in (height) × 8 in (width) = 96 in² (since 20 - 12 = 8)

Wait, no — look again.

The full width is 20 in, and the top part is 12 in wide, so the bottom part extends 8 in beyond on each side? No.

Actually:
- The total height is 12 + 12 = 24 in?
No — looking at the diagram: the top rectangle is 12 in tall and 12 in wide, sitting on a 20 in wide base that is 12 in tall.

So:
- Top rectangle: 12 in × 12 in = 144 in²
- Bottom rectangle: 20 in × 12 in = 240 in²

But they overlap in the 12 in × 12 in region. So total area is:

$$
\text{Top} + \text{Bottom} = 144 + 240 = 384 \text{ in}^2
$$

Wait — but the top rectangle sits on the bottom one, so the total area is just the sum since no overlap subtraction needed.

Yes — it's like a "T" shape.

So total area = 144 + 240 = 384 in²

✔ Area: 384.0 in²

---

6) Rectangle with a triangle on the right

- Rectangle: 20 cm × 20 cm = 400 cm²
- Triangle: base = 10 cm, height = 20 cm

Triangle area = $\frac{1}{2} \times 10 \times 20 = 100$ cm²

Total area = $400 + 100 = 500$ cm²

✔ Area: 500.0 cm²

---

7) Right triangle and a semicircle

- Triangle: legs = 13 ft and 6 ft? Wait — the right angle is between 13 ft and the 6 ft radius?

Looking at the image: There's a right triangle with one leg 13 ft, and a semicircle attached to the hypotenuse? But that seems odd.

Wait — actually, the figure shows:
- A right triangle with vertical leg 13 ft, horizontal leg 6 ft? But there's a semicircle on the base.

Wait — the semicircle has radius 6 ft, so diameter = 12 ft.

But the triangle has a vertical leg of 13 ft, and the base is connected to a semicircle of radius 6 ft → so base is 12 ft.

But is the triangle’s base 12 ft? It looks like the triangle is adjacent to the semicircle.

Actually, likely:
- The triangle has base = 12 ft (same as diameter), height = 13 ft

Wait — but the right angle is shown at the corner.

Wait — let me re-analyze.

From the diagram:
- There is a right triangle with one leg vertical = 13 ft
- The other leg is horizontal, and it connects to a semicircle of radius 6 ft → so the horizontal leg must be 6 ft? But the semicircle has diameter 12 ft.

Ah! Probably the base of the triangle is 12 ft, and the height is 13 ft.

But the right angle is shown at the bottom-left, and the semicircle is on the base.

So:
- Triangle: base = 12 ft, height = 13 ft
- Semicircle: radius = 6 ft

Triangle area = $\frac{1}{2} \times 12 \times 13 = 78$ ft²
Semicircle area = $\frac{1}{2} \pi (6)^2 = \frac{1}{2} \pi \times 36 = 18\pi \approx 56.5$ ft²

Total area = $78 + 56.5 = 134.5$ ft²

✔ Area: 134.5 ft²

---

8) House-shaped figure (triangle on top of rectangle)

- Triangle: base = 6 yd, height = 9 yd
- Rectangle: 6 yd × 3 yd

Triangle area = $\frac{1}{2} \times 6 \times 9 = 27$ yd²
Rectangle area = $6 \times 3 = 18$ yd²

Total area = $27 + 18 = 45$ yd²

✔ Area: 45.0 yd²

---

9) Step-shaped figure

Break into two rectangles:

- Bottom rectangle: 11 ft × 10 ft = 110 ft²
- Top rectangle: 8 ft × 8 ft = 64 ft²

But the top rectangle is on the right side, so we need to make sure dimensions are correct.

From the diagram:
- Total width = 10 ft (bottom)
- Top part is 8 ft wide, 8 ft high
- Bottom part is 11 ft high, but only 10 ft wide? Wait — no.

Wait — the left side is 11 ft high, right side is 8 ft high, and the top is 8 ft long.

So:
- The figure can be split into:
- Left rectangle: 10 ft wide × 8 ft high = 80 ft²
- Right rectangle: 8 ft wide × 8 ft high = 64 ft²
- But wait — the total height is 11 ft on the left, so maybe:

Better:
- Bottom rectangle: 10 ft × 8 ft = 80 ft² (covers the full width up to 8 ft height)
- Top rectangle: 8 ft × 3 ft = 24 ft² (on top of the right side)

Wait — the height difference is 11 - 8 = 3 ft.

So:
- Large rectangle: 10 ft × 8 ft = 80 ft²
- Small rectangle on top: 8 ft × 3 ft = 24 ft²

Total area = $80 + 24 = 104$ ft²

✔ Area: 104.0 ft²

---

✔ Final Answers:

1) 147.0 in²
2) 451.2 cm²
3) 314.1 yd²
4) 73.1 m²
5) 384.0 in²
6) 500.0 cm²
7) 134.5 ft²
8) 45.0 yd²
9) 104.0 ft²

---

Let me know if you'd like this formatted as a printable answer sheet!