Area of Composite Figures Worksheets - Math Monks - 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 figure step by step.

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Figure 1

The shape can be divided into two rectangles:
1. Rectangle 1: \(20 \, \text{ft} \times 5 \, \text{ft}\)
2. Rectangle 2: \(30 \, \text{ft} \times 15 \, \text{ft}\)

Area Calculation:
\[
\text{Area of Rectangle 1} = 20 \times 5 = 100 \, \text{ft}^2
\]
\[
\text{Area of Rectangle 2} = 30 \times 15 = 450 \, \text{ft}^2
\]
\[
\text{Total Area} = 100 + 450 = 550 \, \text{ft}^2
\]

Answer for Figure 1:
\[
\boxed{550}
\]

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Figure 2

The shape can be divided into three rectangles:
1. Rectangle 1: \(30 \, \text{cm} \times 10 \, \text{cm}\)
2. Rectangle 2: \(25 \, \text{cm} \times 10 \, \text{cm}\)
3. Rectangle 3: \(5 \, \text{cm} \times 10 \, \text{cm}\)

Area Calculation:
\[
\text{Area of Rectangle 1} = 30 \times 10 = 300 \, \text{cm}^2
\]
\[
\text{Area of Rectangle 2} = 25 \times 10 = 250 \, \text{cm}^2
\]
\[
\text{Area of Rectangle 3} = 5 \times 10 = 50 \, \text{cm}^2
\]
\[
\text{Total Area} = 300 + 250 + 50 = 600 \, \text{cm}^2
\]

Answer for Figure 2:
\[
\boxed{600}
\]

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Figure 3

The shape can be divided into three rectangles:
1. Rectangle 1: \(36 \, \text{m} \times 24 \, \text{m}\)
2. Rectangle 2: \(14 \, \text{m} \times 10 \, \text{m}\)
3. Rectangle 3: \(10 \, \text{m} \times 10 \, \text{m}\)

Area Calculation:
\[
\text{Area of Rectangle 1} = 36 \times 24 = 864 \, \text{m}^2
\]
\[
\text{Area of Rectangle 2} = 14 \times 10 = 140 \, \text{m}^2
\]
\[
\text{Area of Rectangle 3} = 10 \times 10 = 100 \, \text{m}^2
\]
\[
\text{Total Area} = 864 + 140 + 100 = 1104 \, \text{m}^2
\]

Answer for Figure 3:
\[
\boxed{1104}
\]

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Figure 4

The shape can be divided into three rectangles:
1. Rectangle 1: \(12 \, \text{ft} \times 6 \, \text{ft}\)
2. Rectangle 2: \(3 \, \text{ft} \times 3 \, \text{ft}\)
3. Rectangle 3: \(8 \, \text{ft} \times 3 \, \text{ft}\)

Area Calculation:
\[
\text{Area of Rectangle 1} = 12 \times 6 = 72 \, \text{ft}^2
\]
\[
\text{Area of Rectangle 2} = 3 \times 3 = 9 \, \text{ft}^2
\]
\[
\text{Area of Rectangle 3} = 8 \times 3 = 24 \, \text{ft}^2
\]
\[
\text{Total Area} = 72 + 9 + 24 = 105 \, \text{ft}^2
\]

Answer for Figure 4:
\[
\boxed{105}
\]

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Figure 5

The shape can be divided into three rectangles:
1. Rectangle 1: \(14 \, \text{yd} \times 8 \, \text{yd}\)
2. Rectangle 2: \(8 \, \text{yd} \times 5 \, \text{yd}\)
3. Rectangle 3: \(5 \, \text{yd} \times 8 \, \text{yd}\)

Area Calculation:
\[
\text{Area of Rectangle 1} = 14 \times 8 = 112 \, \text{yd}^2
\]
\[
\text{Area of Rectangle 2} = 8 \times 5 = 40 \, \text{yd}^2
\]
\[
\text{Area of Rectangle 3} = 5 \times 8 = 40 \, \text{yd}^2
\]
\[
\text{Total Area} = 112 + 40 + 40 = 192 \, \text{yd}^2
\]

Answer for Figure 5:
\[
\boxed{192}
\]

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Figure 6

The shape can be divided into three rectangles:
1. Rectangle 1: \(28 \, \text{m} \times 18 \, \text{m}\)
2. Rectangle 2: \(12 \, \text{m} \times 6 \, \text{m}\)
3. Rectangle 3: \(10 \, \text{m} \times 6 \, \text{m}\)

Area Calculation:
\[
\text{Area of Rectangle 1} = 28 \times 18 = 504 \, \text{m}^2
\]
\[
\text{Area of Rectangle 2} = 12 \times 6 = 72 \, \text{m}^2
\]
\[
\text{Area of Rectangle 3} = 10 \times 6 = 60 \, \text{m}^2
\]
\[
\text{Total Area} = 504 + 72 + 60 = 636 \, \text{m}^2
\]

Answer for Figure 6:
\[
\boxed{636}
\]

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Figure 7

The shape can be divided into four rectangles:
1. Rectangle 1: \(6 \, \text{mm} \times 2 \, \text{mm}\)
2. Rectangle 2: \(3 \, \text{mm} \times 1 \, \text{mm}\)
3. Rectangle 3: \(3 \, \text{mm} \times 3 \, \text{mm}\)
4. Rectangle 4: \(8 \, \text{mm} \times 2 \, \text{mm}\)

Area Calculation:
\[
\text{Area of Rectangle 1} = 6 \times 2 = 12 \, \text{mm}^2
\]
\[
\text{Area of Rectangle 2} = 3 \times 1 = 3 \, \text{mm}^2
\]
\[
\text{Area of Rectangle 3} = 3 \times 3 = 9 \, \text{mm}^2
\]
\[
\text{Area of Rectangle 4} = 8 \times 2 = 16 \, \text{mm}^2
\]
\[
\text{Total Area} = 12 + 3 + 9 + 16 = 40 \, \text{mm}^2
\]

Answer for Figure 7:
\[
\boxed{40}
\]

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Figure 8

The shape is a large rectangle with a smaller rectangle removed from it:
1. Large Rectangle: \(28 \, \text{cm} \times 16 \, \text{cm}\)
2. Small Rectangle: \(18 \, \text{cm} \times 6 \, \text{cm}\)

Area Calculation:
\[
\text{Area of Large Rectangle} = 28 \times 16 = 448 \, \text{cm}^2
\]
\[
\text{Area of Small Rectangle} = 18 \times 6 = 108 \, \text{cm}^2
\]
\[
\text{Total Area} = 448 - 108 = 340 \, \text{cm}^2
\]

Answer for Figure 8:
\[
\boxed{340}
\]

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Final Answers:

\[
\boxed{550, 600, 1104, 105, 192, 636, 40, 340}
\]