Finding Area Of Composite Figures Worksheet - Free Printable

To solve the problem of finding the area of composite rectangles, we need to break each shape into simpler rectangular parts, calculate the area of each part, and then sum these areas. Let's go through each problem step by step.

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Problem 1:

The shape is composed of two rectangles:
- Rectangle 1: \(20 \, \text{ft} \times 5 \, \text{ft}\)
- Rectangle 2: \(30 \, \text{ft} \times 1.5 \, \text{ft}\)

Step 1: Calculate the area of Rectangle 1.
\[
\text{Area}_1 = 20 \, \text{ft} \times 5 \, \text{ft} = 100 \, \text{ft}^2
\]

Step 2: Calculate the area of Rectangle 2.
\[
\text{Area}_2 = 30 \, \text{ft} \times 1.5 \, \text{ft} = 45 \, \text{ft}^2
\]

Step 3: Sum the areas.
\[
\text{Total Area} = \text{Area}_1 + \text{Area}_2 = 100 \, \text{ft}^2 + 45 \, \text{ft}^2 = 145 \, \text{ft}^2
\]

Answer for Problem 1:
\[
\boxed{145 \, \text{ft}^2}
\]

---

Problem 2:

The shape is composed of three rectangles:
- Rectangle 1: \(30 \, \text{cm} \times 25 \, \text{cm}\)
- Rectangle 2: \(10 \, \text{cm} \times 5 \, \text{cm}\)
- Rectangle 3: \(10 \, \text{cm} \times 10 \, \text{cm}\)

Step 1: Calculate the area of Rectangle 1.
\[
\text{Area}_1 = 30 \, \text{cm} \times 25 \, \text{cm} = 750 \, \text{cm}^2
\]

Step 2: Calculate the area of Rectangle 2.
\[
\text{Area}_2 = 10 \, \text{cm} \times 5 \, \text{cm} = 50 \, \text{cm}^2
\]

Step 3: Calculate the area of Rectangle 3.
\[
\text{Area}_3 = 10 \, \text{cm} \times 10 \, \text{cm} = 100 \, \text{cm}^2
\]

Step 4: Sum the areas.
\[
\text{Total Area} = \text{Area}_1 + \text{Area}_2 + \text{Area}_3 = 750 \, \text{cm}^2 + 50 \, \text{cm}^2 + 100 \, \text{cm}^2 = 900 \, \text{cm}^2
\]

Answer for Problem 2:
\[
\boxed{900 \, \text{cm}^2}
\]

---

Problem 3:

The shape is composed of three rectangles:
- Rectangle 1: \(36 \, \text{m} \times 24 \, \text{m}\)
- Rectangle 2: \(14 \, \text{m} \times 10 \, \text{m}\)
- Rectangle 3: \(10 \, \text{m} \times 10 \, \text{m}\)

Step 1: Calculate the area of Rectangle 1.
\[
\text{Area}_1 = 36 \, \text{m} \times 24 \, \text{m} = 864 \, \text{m}^2
\]

Step 2: Calculate the area of Rectangle 2.
\[
\text{Area}_2 = 14 \, \text{m} \times 10 \, \text{m} = 140 \, \text{m}^2
\]

Step 3: Calculate the area of Rectangle 3.
\[
\text{Area}_3 = 10 \, \text{m} \times 10 \, \text{m} = 100 \, \text{m}^2
\]

Step 4: Sum the areas.
\[
\text{Total Area} = \text{Area}_1 + \text{Area}_2 + \text{Area}_3 = 864 \, \text{m}^2 + 140 \, \text{m}^2 + 100 \, \text{m}^2 = 1104 \, \text{m}^2
\]

Answer for Problem 3:
\[
\boxed{1104 \, \text{m}^2}
\]

---

Problem 4:

The shape is composed of two rectangles:
- Rectangle 1: \(12 \, \text{ft} \times 3 \, \text{ft}\)
- Rectangle 2: \(8 \, \text{ft} \times 6 \, \text{ft}\)

Step 1: Calculate the area of Rectangle 1.
\[
\text{Area}_1 = 12 \, \text{ft} \times 3 \, \text{ft} = 36 \, \text{ft}^2
\]

Step 2: Calculate the area of Rectangle 2.
\[
\text{Area}_2 = 8 \, \text{ft} \times 6 \, \text{ft} = 48 \, \text{ft}^2
\]

Step 3: Sum the areas.
\[
\text{Total Area} = \text{Area}_1 + \text{Area}_2 = 36 \, \text{ft}^2 + 48 \, \text{ft}^2 = 84 \, \text{ft}^2
\]

Answer for Problem 4:
\[
\boxed{84 \, \text{ft}^2}
\]

---

Problem 5:

The shape is composed of three rectangles:
- Rectangle 1: \(14 \, \text{yd} \times 8 \, \text{yd}\)
- Rectangle 2: \(5 \, \text{yd} \times 5 \, \text{yd}\)
- Rectangle 3: \(5 \, \text{yd} \times 5 \, \text{yd}\)

Step 1: Calculate the area of Rectangle 1.
\[
\text{Area}_1 = 14 \, \text{yd} \times 8 \, \text{yd} = 112 \, \text{yd}^2
\]

Step 2: Calculate the area of Rectangle 2.
\[
\text{Area}_2 = 5 \, \text{yd} \times 5 \, \text{yd} = 25 \, \text{yd}^2
\]

Step 3: Calculate the area of Rectangle 3.
\[
\text{Area}_3 = 5 \, \text{yd} \times 5 \, \text{yd} = 25 \, \text{yd}^2
\]

Step 4: Sum the areas.
\[
\text{Total Area} = \text{Area}_1 + \text{Area}_2 + \text{Area}_3 = 112 \, \text{yd}^2 + 25 \, \text{yd}^2 + 25 \, \text{yd}^2 = 162 \, \text{yd}^2
\]

Answer for Problem 5:
\[
\boxed{162 \, \text{yd}^2}
\]

---

Problem 6:

The shape is composed of three rectangles:
- Rectangle 1: \(28 \, \text{m} \times 12 \, \text{m}\)
- Rectangle 2: \(10 \, \text{m} \times 6 \, \text{m}\)
- Rectangle 3: \(18 \, \text{m} \times 6 \, \text{m}\)

Step 1: Calculate the area of Rectangle 1.
\[
\text{Area}_1 = 28 \, \text{m} \times 12 \, \text{m} = 336 \, \text{m}^2
\]

Step 2: Calculate the area of Rectangle 2.
\[
\text{Area}_2 = 10 \, \text{m} \times 6 \, \text{m} = 60 \, \text{m}^2
\]

Step 3: Calculate the area of Rectangle 3.
\[
\text{Area}_3 = 18 \, \text{m} \times 6 \, \text{m} = 108 \, \text{m}^2
\]

Step 4: Sum the areas.
\[
\text{Total Area} = \text{Area}_1 + \text{Area}_2 + \text{Area}_3 = 336 \, \text{m}^2 + 60 \, \text{m}^2 + 108 \, \text{m}^2 = 504 \, \text{m}^2
\]

Answer for Problem 6:
\[
\boxed{504 \, \text{m}^2}
\]

---

Problem 7:

The shape is composed of three rectangles:
- Rectangle 1: \(8 \, \text{mm} \times 6 \, \text{mm}\)
- Rectangle 2: \(3 \, \text{mm} \times 2 \, \text{mm}\)
- Rectangle 3: \(1 \, \text{mm} \times 3 \, \text{mm}\)

Step 1: Calculate the area of Rectangle 1.
\[
\text{Area}_1 = 8 \, \text{mm} \times 6 \, \text{mm} = 48 \, \text{mm}^2
\]

Step 2: Calculate the area of Rectangle 2.
\[
\text{Area}_2 = 3 \, \text{mm} \times 2 \, \text{mm} = 6 \, \text{mm}^2
\]

Step 3: Calculate the area of Rectangle 3.
\[
\text{Area}_3 = 1 \, \text{mm} \times 3 \, \text{mm} = 3 \, \text{mm}^2
\]

Step 4: Sum the areas.
\[
\text{Total Area} = \text{Area}_1 + \text{Area}_2 + \text{Area}_3 = 48 \, \text{mm}^2 + 6 \, \text{mm}^2 + 3 \, \text{mm}^2 = 57 \, \text{mm}^2
\]

Answer for Problem 7:
\[
\boxed{57 \, \text{mm}^2}
\]

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Problem 8:

The shape is a large rectangle with a smaller rectangle removed from it:
- Large Rectangle: \(28 \, \text{cm} \times 16 \, \text{cm}\)
- Small Rectangle: \(8 \, \text{cm} \times 6 \, \text{cm}\)

Step 1: Calculate the area of the large rectangle.
\[
\text{Area}_{\text{large}} = 28 \, \text{cm} \times 16 \, \text{cm} = 448 \, \text{cm}^2
\]

Step 2: Calculate the area of the small rectangle.
\[
\text{Area}_{\text{small}} = 8 \, \text{cm} \times 6 \, \text{cm} = 48 \, \text{cm}^2
\]

Step 3: Subtract the area of the small rectangle from the area of the large rectangle.
\[
\text{Total Area} = \text{Area}_{\text{large}} - \text{Area}_{\text{small}} = 448 \, \text{cm}^2 - 48 \, \text{cm}^2 = 400 \, \text{cm}^2
\]

Answer for Problem 8:
\[
\boxed{400 \, \text{cm}^2}
\]

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Final Answers:

\[
\boxed{145 \, \text{ft}^2, 900 \, \text{cm}^2, 1104 \, \text{m}^2, 84 \, \text{ft}^2, 162 \, \text{yd}^2, 504 \, \text{m}^2, 57 \, \text{mm}^2, 400 \, \text{cm}^2}
\]