Area of Compound Shapes Textbook Exercise - Corbettmaths - Free Printable
Educational worksheet: Area of Compound Shapes Textbook Exercise - Corbettmaths. Download and print for classroom or home learning activities.
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Step-by-step solution for: Area of Compound Shapes Textbook Exercise - Corbettmaths
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Show Answer Key & Explanations
Step-by-step solution for: Area of Compound Shapes Textbook Exercise - Corbettmaths
To solve the problem of finding the area of each compound shape, we need to break down each shape into simpler geometric shapes (like rectangles) and then calculate the total area by summing up the areas of these simpler shapes. Let's go through each shape step by step.
---
The shape can be divided into two rectangles:
1. A rectangle with dimensions \(9 \, \text{cm} \times 8 \, \text{cm}\).
2. A smaller rectangle with dimensions \(7 \, \text{cm} \times 5 \, \text{cm}\).
However, the overlapping part (the smaller rectangle) is already included in the larger rectangle, so we only need to add the area of the smaller rectangle that extends beyond the larger one.
- Area of the larger rectangle: \(9 \times 8 = 72 \, \text{cm}^2\).
- Area of the smaller rectangle: \(7 \times 5 = 35 \, \text{cm}^2\).
Since the smaller rectangle is entirely within the larger rectangle, the total area is simply the area of the larger rectangle:
\[
\text{Total area} = 72 \, \text{cm}^2
\]
---
The shape can be divided into three rectangles:
1. A large rectangle with dimensions \(25 \, \text{cm} \times 12 \, \text{cm}\).
2. A smaller rectangle with dimensions \(6 \, \text{cm} \times 10 \, \text{cm}\).
- Area of the large rectangle: \(25 \times 12 = 300 \, \text{cm}^2\).
- Area of the smaller rectangle: \(6 \times 10 = 60 \, \text{cm}^2\).
The total area is the sum of these two areas:
\[
\text{Total area} = 300 + 60 = 360 \, \text{cm}^2
\]
---
The shape can be divided into two rectangles:
1. A larger rectangle with dimensions \(13 \, \text{cm} \times 10 \, \text{cm}\).
2. A smaller rectangle with dimensions \(4 \, \text{cm} \times 3 \, \text{cm}\).
- Area of the larger rectangle: \(13 \times 10 = 130 \, \text{cm}^2\).
- Area of the smaller rectangle: \(4 \times 3 = 12 \, \text{cm}^2\).
The total area is the sum of these two areas:
\[
\text{Total area} = 130 + 12 = 142 \, \text{cm}^2
\]
---
The shape can be divided into three rectangles:
1. A large rectangle with dimensions \(9 \, \text{cm} \times 3 \, \text{cm}\).
2. A smaller rectangle with dimensions \(4 \, \text{cm} \times 2 \, \text{cm}\).
3. Another smaller rectangle with dimensions \(5 \, \text{cm} \times 2 \, \text{cm}\).
- Area of the large rectangle: \(9 \times 3 = 27 \, \text{cm}^2\).
- Area of the first smaller rectangle: \(4 \times 2 = 8 \, \text{cm}^2\).
- Area of the second smaller rectangle: \(5 \times 2 = 10 \, \text{cm}^2\).
The total area is the sum of these three areas:
\[
\text{Total area} = 27 + 8 + 10 = 45 \, \text{cm}^2
\]
---
The shape can be divided into one large rectangle and three smaller rectangles:
1. A large rectangle with dimensions \(24 \, \text{cm} \times 20 \, \text{cm}\).
2. Three smaller rectangles with dimensions \(6 \, \text{cm} \times 8 \, \text{cm}\), \(6 \, \text{cm} \times 8 \, \text{cm}\), and \(2 \, \text{cm} \times 8 \, \text{cm}\).
- Area of the large rectangle: \(24 \times 20 = 480 \, \text{cm}^2\).
- Area of the first smaller rectangle: \(6 \times 8 = 48 \, \text{cm}^2\).
- Area of the second smaller rectangle: \(6 \times 8 = 48 \, \text{cm}^2\).
- Area of the third smaller rectangle: \(2 \times 8 = 16 \, \text{cm}^2\).
The total area is the area of the large rectangle minus the areas of the three smaller rectangles:
\[
\text{Total area} = 480 - (48 + 48 + 16) = 480 - 112 = 368 \, \text{cm}^2
\]
---
The shape can be divided into one large rectangle and two smaller rectangles:
1. A large rectangle with dimensions \(8 \, \text{cm} \times 7 \, \text{cm}\).
2. Two smaller rectangles with dimensions \(2 \, \text{cm} \times 3 \, \text{cm}\) and \(3 \, \text{cm} \times 3 \, \text{cm}\).
- Area of the large rectangle: \(8 \times 7 = 56 \, \text{cm}^2\).
- Area of the first smaller rectangle: \(2 \times 3 = 6 \, \text{cm}^2\).
- Area of the second smaller rectangle: \(3 \times 3 = 9 \, \text{cm}^2\).
The total area is the area of the large rectangle minus the areas of the two smaller rectangles:
\[
\text{Total area} = 56 - (6 + 9) = 56 - 15 = 41 \, \text{cm}^2
\]
---
\[
\boxed{72, 360, 142, 45, 368, 41}
\]
---
Shape (a)
The shape can be divided into two rectangles:
1. A rectangle with dimensions \(9 \, \text{cm} \times 8 \, \text{cm}\).
2. A smaller rectangle with dimensions \(7 \, \text{cm} \times 5 \, \text{cm}\).
However, the overlapping part (the smaller rectangle) is already included in the larger rectangle, so we only need to add the area of the smaller rectangle that extends beyond the larger one.
- Area of the larger rectangle: \(9 \times 8 = 72 \, \text{cm}^2\).
- Area of the smaller rectangle: \(7 \times 5 = 35 \, \text{cm}^2\).
Since the smaller rectangle is entirely within the larger rectangle, the total area is simply the area of the larger rectangle:
\[
\text{Total area} = 72 \, \text{cm}^2
\]
---
Shape (b)
The shape can be divided into three rectangles:
1. A large rectangle with dimensions \(25 \, \text{cm} \times 12 \, \text{cm}\).
2. A smaller rectangle with dimensions \(6 \, \text{cm} \times 10 \, \text{cm}\).
- Area of the large rectangle: \(25 \times 12 = 300 \, \text{cm}^2\).
- Area of the smaller rectangle: \(6 \times 10 = 60 \, \text{cm}^2\).
The total area is the sum of these two areas:
\[
\text{Total area} = 300 + 60 = 360 \, \text{cm}^2
\]
---
Shape (c)
The shape can be divided into two rectangles:
1. A larger rectangle with dimensions \(13 \, \text{cm} \times 10 \, \text{cm}\).
2. A smaller rectangle with dimensions \(4 \, \text{cm} \times 3 \, \text{cm}\).
- Area of the larger rectangle: \(13 \times 10 = 130 \, \text{cm}^2\).
- Area of the smaller rectangle: \(4 \times 3 = 12 \, \text{cm}^2\).
The total area is the sum of these two areas:
\[
\text{Total area} = 130 + 12 = 142 \, \text{cm}^2
\]
---
Shape (d)
The shape can be divided into three rectangles:
1. A large rectangle with dimensions \(9 \, \text{cm} \times 3 \, \text{cm}\).
2. A smaller rectangle with dimensions \(4 \, \text{cm} \times 2 \, \text{cm}\).
3. Another smaller rectangle with dimensions \(5 \, \text{cm} \times 2 \, \text{cm}\).
- Area of the large rectangle: \(9 \times 3 = 27 \, \text{cm}^2\).
- Area of the first smaller rectangle: \(4 \times 2 = 8 \, \text{cm}^2\).
- Area of the second smaller rectangle: \(5 \times 2 = 10 \, \text{cm}^2\).
The total area is the sum of these three areas:
\[
\text{Total area} = 27 + 8 + 10 = 45 \, \text{cm}^2
\]
---
Shape (e)
The shape can be divided into one large rectangle and three smaller rectangles:
1. A large rectangle with dimensions \(24 \, \text{cm} \times 20 \, \text{cm}\).
2. Three smaller rectangles with dimensions \(6 \, \text{cm} \times 8 \, \text{cm}\), \(6 \, \text{cm} \times 8 \, \text{cm}\), and \(2 \, \text{cm} \times 8 \, \text{cm}\).
- Area of the large rectangle: \(24 \times 20 = 480 \, \text{cm}^2\).
- Area of the first smaller rectangle: \(6 \times 8 = 48 \, \text{cm}^2\).
- Area of the second smaller rectangle: \(6 \times 8 = 48 \, \text{cm}^2\).
- Area of the third smaller rectangle: \(2 \times 8 = 16 \, \text{cm}^2\).
The total area is the area of the large rectangle minus the areas of the three smaller rectangles:
\[
\text{Total area} = 480 - (48 + 48 + 16) = 480 - 112 = 368 \, \text{cm}^2
\]
---
Shape (f)
The shape can be divided into one large rectangle and two smaller rectangles:
1. A large rectangle with dimensions \(8 \, \text{cm} \times 7 \, \text{cm}\).
2. Two smaller rectangles with dimensions \(2 \, \text{cm} \times 3 \, \text{cm}\) and \(3 \, \text{cm} \times 3 \, \text{cm}\).
- Area of the large rectangle: \(8 \times 7 = 56 \, \text{cm}^2\).
- Area of the first smaller rectangle: \(2 \times 3 = 6 \, \text{cm}^2\).
- Area of the second smaller rectangle: \(3 \times 3 = 9 \, \text{cm}^2\).
The total area is the area of the large rectangle minus the areas of the two smaller rectangles:
\[
\text{Total area} = 56 - (6 + 9) = 56 - 15 = 41 \, \text{cm}^2
\]
---
Final Answers
\[
\boxed{72, 360, 142, 45, 368, 41}
\]
Parent Tip: Review the logic above to help your child master the concept of compound shapes worksheet.
