Math worksheet for calculating the area of compound shapes, featuring nine geometric figures with labeled dimensions.

Here are the step-by-step solutions for finding the area of each compound shape.

1) Trapezoid
* Formula: Area = $\frac{(base_1 + base_2)}{2} \times height$
* Values: Base 1 = 14 in, Base 2 = 7 in, Height = 14 in
* Calculation:
* Add bases: $14 + 7 = 21$
* Divide by 2: $21 / 2 = 10.5$
* Multiply by height: $10.5 \times 14 = 147$
* Area: 147 sq in

2) Rectangle with Semicircle on top
* Rectangle Part:
* Area = $width \times height$
* $18 \text{ cm} \times 18 \text{ cm} = 324 \text{ sq cm}$
* Semicircle Part:
* Diameter is 18 cm, so Radius ($r$) is 9 cm.
* Area of full circle = $\pi \times r^2 = 3.14159 \times 9^2 = 3.14159 \times 81 \approx 254.47$
* Area of semicircle = $254.47 / 2 \approx 127.23$
* Total Area: $324 + 127.23 = 451.23$
* Rounded: 451.2 sq cm

3) Rectangle with Semicircle on top
* Rectangle Part:
* Area = $20 \text{ yd} \times 15 \text{ yd} = 300 \text{ sq yd}$
* Semicircle Part:
* Diameter is 6 yd, so Radius ($r$) is 3 yd.
* Area of full circle = $\pi \times 3^2 = 3.14159 \times 9 \approx 28.27$
* Area of semicircle = $28.27 / 2 \approx 14.14$
* Total Area: $300 + 14.14 = 314.14$
* Rounded: 314.1 sq yd

4) Triangle on top of a Semicircle
* Triangle Part:
* Base = 8 m, Height = 12 m
* Area = $\frac{1}{2} \times base \times height = 0.5 \times 8 \times 12 = 48 \text{ sq m}$
* Semicircle Part:
* Diameter is 8 m, so Radius ($r$) is 4 m.
* Area of full circle = $\pi \times 4^2 = 3.14159 \times 16 \approx 50.27$
* Area of semicircle = $50.27 / 2 \approx 25.13$
* Total Area: $48 + 25.13 = 73.13$
* Rounded: 73.1 sq m

5) T-Shaped Figure (Two Rectangles)
* Top Rectangle:
* $12 \text{ in} \times 12 \text{ in} = 144 \text{ sq in}$
* Bottom Rectangle:
* $20 \text{ in} \times 12 \text{ in} = 240 \text{ sq in}$
* Total Area: $144 + 240 = 384$
* Area: 384 sq in

6) Rectangle attached to a Triangle
* Rectangle Part:
* $20 \text{ cm} \times 20 \text{ cm} = 400 \text{ sq cm}$
* Triangle Part:
* The triangle shares the side of the rectangle, so its base is 20 cm. Its height is given as 10 cm.
* Area = $\frac{1}{2} \times 20 \times 10 = 100 \text{ sq cm}$
* Total Area: $400 + 100 = 500$
* Area: 500 sq cm

7) Triangle next to a Semicircle
* Triangle Part:
* Base = 6 ft, Height = 13 ft
* Area = $\frac{1}{2} \times 6 \times 13 = 39 \text{ sq ft}$
* Semicircle Part:
* Diameter is 6 ft, so Radius ($r$) is 3 ft.
* Area of full circle = $\pi \times 3^2 \approx 28.27$
* Area of semicircle = $28.27 / 2 \approx 14.14$
* Total Area: $39 + 14.14 = 53.14$
* Rounded: 53.1 sq ft

8) House Shape (Rectangle + Triangle)
* Rectangle Part:
* Width = 6 yd, Height = 6 yd
* Area = $6 \times 6 = 36 \text{ sq yd}$
* Triangle Part:
* Base = 6 yd (same as rectangle width), Height = 9 yd
* Area = $\frac{1}{2} \times 6 \times 9 = 27 \text{ sq yd}$
* Total Area: $36 + 27 = 63$
* Area: 63 sq yd

9) L-Shaped Figure (Two Rectangles)
* We can split this into two vertical rectangles.
* Left Rectangle:
* Width = 10 ft, Height = 11 ft
* Area = $10 \times 11 = 110 \text{ sq ft}$
* Right Rectangle:
* Width = 8 ft. To find the height, look at the left side (11 ft) and subtract the top part of the right side that isn't there? No, simpler way: The total height on the left is 11. The height of the right block is labeled 8 ft.
* Area = $8 \times 8 = 64 \text{ sq ft}$
* Total Area: $110 + 64 = 174$
* Area: 174 sq ft

Final Answer:
1) 147 sq in
2) 451.2 sq cm
3) 314.1 sq yd
4) 73.1 sq m
5) 384 sq in
6) 500 sq cm
7) 53.1 sq ft
8) 63 sq yd
9) 174 sq ft