Worksheet for calculating the area of compound shapes with examples and practice questions.
A worksheet titled "Area of Compound Shapes" with six labeled diagrams (a-f) showing various compound shapes with dimensions, including a play button and QR code for a video on Corbettmaths.com.
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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 part step by step.
---
#### (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 \(5 \, \text{cm} \times 7 \, \text{cm}\).
Area Calculation:
- Area of the larger rectangle: \(9 \times 8 = 72 \, \text{cm}^2\).
- Area of the smaller rectangle: \(5 \times 7 = 35 \, \text{cm}^2\).
Total area:
\[
72 + 35 = 107 \, \text{cm}^2
\]
#### (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 Calculation:
- Area of the large rectangle: \(25 \times 12 = 300 \, \text{cm}^2\).
- Area of the smaller rectangle: \(6 \times 10 = 60 \, \text{cm}^2\).
Total area:
\[
300 + 60 = 360 \, \text{cm}^2
\]
#### (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 Calculation:
- Area of the larger rectangle: \(13 \times 10 = 130 \, \text{cm}^2\).
- Area of the smaller rectangle: \(4 \times 3 = 12 \, \text{cm}^2\).
Total area:
\[
130 - 12 = 118 \, \text{cm}^2
\]
(Note: The smaller rectangle is subtracted because it is a cut-out section.)
#### (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 Calculation:
- 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: \(5 \times 2 = 10 \, \text{cm}^2\).
Total area:
\[
27 + 8 + 10 = 45 \, \text{cm}^2
\]
#### (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 Calculation:
- 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: \(2 \times 8 = 16 \, \text{cm}^2\).
Total area of the smaller rectangles:
\[
48 + 48 + 16 = 112 \, \text{cm}^2
\]
Subtract the total area of the smaller rectangles from the large rectangle:
\[
480 - 112 = 368 \, \text{cm}^2
\]
#### (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 Calculation:
- 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: \(3 \times 3 = 9 \, \text{cm}^2\).
Total area of the smaller rectangles:
\[
6 + 9 = 15 \, \text{cm}^2
\]
Subtract the total area of the smaller rectangles from the large rectangle:
\[
56 - 15 = 41 \, \text{cm}^2
\]
---
\[
\boxed{107, 360, 118, 45, 368, 41}
\]
---
Question 1: Work out the area of each of these shapes.
#### (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 \(5 \, \text{cm} \times 7 \, \text{cm}\).
Area Calculation:
- Area of the larger rectangle: \(9 \times 8 = 72 \, \text{cm}^2\).
- Area of the smaller rectangle: \(5 \times 7 = 35 \, \text{cm}^2\).
Total area:
\[
72 + 35 = 107 \, \text{cm}^2
\]
#### (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 Calculation:
- Area of the large rectangle: \(25 \times 12 = 300 \, \text{cm}^2\).
- Area of the smaller rectangle: \(6 \times 10 = 60 \, \text{cm}^2\).
Total area:
\[
300 + 60 = 360 \, \text{cm}^2
\]
#### (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 Calculation:
- Area of the larger rectangle: \(13 \times 10 = 130 \, \text{cm}^2\).
- Area of the smaller rectangle: \(4 \times 3 = 12 \, \text{cm}^2\).
Total area:
\[
130 - 12 = 118 \, \text{cm}^2
\]
(Note: The smaller rectangle is subtracted because it is a cut-out section.)
#### (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 Calculation:
- 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: \(5 \times 2 = 10 \, \text{cm}^2\).
Total area:
\[
27 + 8 + 10 = 45 \, \text{cm}^2
\]
#### (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 Calculation:
- 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: \(2 \times 8 = 16 \, \text{cm}^2\).
Total area of the smaller rectangles:
\[
48 + 48 + 16 = 112 \, \text{cm}^2
\]
Subtract the total area of the smaller rectangles from the large rectangle:
\[
480 - 112 = 368 \, \text{cm}^2
\]
#### (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 Calculation:
- 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: \(3 \times 3 = 9 \, \text{cm}^2\).
Total area of the smaller rectangles:
\[
6 + 9 = 15 \, \text{cm}^2
\]
Subtract the total area of the smaller rectangles from the large rectangle:
\[
56 - 15 = 41 \, \text{cm}^2
\]
---
Final Answers:
\[
\boxed{107, 360, 118, 45, 368, 41}
\]
Parent Tip: Review the logic above to help your child master the concept of composite shapes worksheet.
