Compound Figures Worksheet - Printable Fitness Fusion Hub - Free Printable

To solve the problem of finding the area of each composite figure, we need to break down each figure into simpler shapes (such as rectangles, triangles, or trapezoids) and then calculate the area of each part before summing them up. Let's go through each figure step by step.

---

Problem 1:

The figure is a rectangle with a smaller rectangle removed from one corner.

- Step 1: Calculate the area of the large rectangle.
\[
\text{Area of large rectangle} = \text{length} \times \text{width} = 10 \times 8 = 80 \, \text{in}^2
\]

- Step 2: Calculate the area of the smaller rectangle that is removed.
\[
\text{Area of smaller rectangle} = \text{length} \times \text{width} = 2 \times 7 = 14 \, \text{in}^2
\]

- Step 3: Subtract the area of the smaller rectangle from the area of the large rectangle.
\[
\text{Total area} = 80 - 14 = 66 \, \text{in}^2
\]

Answer for Problem 1:
\[
\boxed{66}
\]

---

Problem 2:

The figure consists of two rectangles joined together.

- Step 1: Calculate the area of the top rectangle.
\[
\text{Area of top rectangle} = \text{length} \times \text{width} = 30 \times 12 = 360 \, \text{in}^2
\]

- Step 2: Calculate the area of the bottom rectangle.
\[
\text{Area of bottom rectangle} = \text{length} \times \text{width} = 10 \times 5 = 50 \, \text{in}^2
\]

- Step 3: Add the areas of the two rectangles.
\[
\text{Total area} = 360 + 50 = 410 \, \text{in}^2
\]

Answer for Problem 2:
\[
\boxed{410}
\]

---

Problem 3:

The figure is a large rectangle with three smaller rectangles removed.

- Step 1: Calculate the area of the large rectangle.
\[
\text{Area of large rectangle} = \text{length} \times \text{width} = 70 \times 50 = 3500 \, \text{in}^2
\]

- Step 2: Calculate the area of the first smaller rectangle.
\[
\text{Area of first smaller rectangle} = \text{length} \times \text{width} = 30 \times 30 = 900 \, \text{in}^2
\]

- Step 3: Calculate the area of the second smaller rectangle.
\[
\text{Area of second smaller rectangle} = \text{length} \times \text{width} = 30 \times 30 = 900 \, \text{in}^2
\]

- Step 4: Calculate the area of the third smaller rectangle.
\[
\text{Area of third smaller rectangle} = \text{length} \times \text{width} = 40 \times 10 = 400 \, \text{in}^2
\]

- Step 5: Subtract the areas of the three smaller rectangles from the area of the large rectangle.
\[
\text{Total area} = 3500 - (900 + 900 + 400) = 3500 - 2200 = 1300 \, \text{in}^2
\]

Answer for Problem 3:
\[
\boxed{1300}
\]

---

Problem 4:

The figure is a combination of a rectangle and a triangle.

- Step 1: Calculate the area of the rectangle.
\[
\text{Area of rectangle} = \text{length} \times \text{width} = 24 \times 10 = 240 \, \text{in}^2
\]

- Step 2: Calculate the area of the triangle.
\[
\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 24 \times 9 = 108 \, \text{in}^2
\]

- Step 3: Add the areas of the rectangle and the triangle.
\[
\text{Total area} = 240 + 108 = 348 \, \text{in}^2
\]

Answer for Problem 4:
\[
\boxed{348}
\]

---

Problem 5:

The figure is a trapezoid.

- Step 1: Use the formula for the area of a trapezoid:
\[
\text{Area of trapezoid} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}
\]
Here, \(\text{Base}_1 = 28 \, \text{in}\), \(\text{Base}_2 = 12 \, \text{in}\), and \(\text{Height} = 4 \, \text{in}\).

- Step 2: Substitute the values into the formula.
\[
\text{Area} = \frac{1}{2} \times (28 + 12) \times 4 = \frac{1}{2} \times 40 \times 4 = 80 \, \text{in}^2
\]

Answer for Problem 5:
\[
\boxed{80}
\]

---

Problem 6:

The figure is a large rectangle with a right triangle removed.

- Step 1: Calculate the area of the large rectangle.
\[
\text{Area of large rectangle} = \text{length} \times \text{width} = 50 \times 40 = 2000 \, \text{in}^2
\]

- Step 2: Calculate the area of the right triangle.
\[
\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 20 \times 18 = 180 \, \text{in}^2
\]

- Step 3: Subtract the area of the triangle from the area of the rectangle.
\[
\text{Total area} = 2000 - 180 = 1820 \, \text{in}^2
\]

Answer for Problem 6:
\[
\boxed{1820}
\]

---

Final Answers:

\[
\boxed{66, 410, 1300, 348, 80, 1820}
\]