This worksheet from Corbettmaths features six different compound shapes, ranging from L-shapes to inverted T-shapes, asking students to calculate the total area based on the provided side lengths.
Corbettmaths worksheet showing six compound shapes labeled a to f with dimensions for calculating area.
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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 \(5 \, \text{cm} \times 7 \, \text{cm}\).
However, the smaller rectangle overlaps with the larger one, so we only need to consider the part that is not already included in the larger rectangle. The effective additional area is a rectangle with dimensions \(5 \, \text{cm} \times (8 - 5) = 5 \, \text{cm} \times 3 \, \text{cm}\).
- Area of the larger rectangle: \(9 \times 8 = 72 \, \text{cm}^2\).
- Area of the smaller rectangle (additional part): \(5 \times 3 = 15 \, \text{cm}^2\).
Total area:
\[
72 + 15 = 87 \, \text{cm}^2
\]
---
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 \(6 \, \text{cm} \times 10 \, \text{cm}\).
The total area is the sum of the areas of these rectangles:
- 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:
\[
300 + 60 = 360 \, \text{cm}^2
\]
---
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 \(4 \, \text{cm} \times 3 \, \text{cm}\).
However, the smaller rectangle is subtracted from the larger one because it is a cut-out section. The effective area is:
- 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:
\[
130 - 12 = 118 \, \text{cm}^2
\]
---
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 \(5 \, \text{cm} \times 2 \, \text{cm}\).
The total area is the sum of the areas of these rectangles:
- 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:
\[
27 + 8 + 10 = 45 \, \text{cm}^2
\]
---
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 \(2 \, \text{cm} \times 8 \, \text{cm}\).
The total area is the area of the large rectangle minus the areas of the three smaller rectangles:
- 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:
\[
480 - (48 + 48 + 16) = 480 - 112 = 368 \, \text{cm}^2
\]
---
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 \(3 \, \text{cm} \times 3 \, \text{cm}\).
The total area is the area of the large rectangle minus the areas of the two smaller rectangles:
- 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:
\[
56 - (6 + 9) = 56 - 15 = 41 \, \text{cm}^2
\]
---
\[
\boxed{87, 360, 118, 45, 368, 41}
\]
---
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 \(5 \, \text{cm} \times 7 \, \text{cm}\).
However, the smaller rectangle overlaps with the larger one, so we only need to consider the part that is not already included in the larger rectangle. The effective additional area is a rectangle with dimensions \(5 \, \text{cm} \times (8 - 5) = 5 \, \text{cm} \times 3 \, \text{cm}\).
- Area of the larger rectangle: \(9 \times 8 = 72 \, \text{cm}^2\).
- Area of the smaller rectangle (additional part): \(5 \times 3 = 15 \, \text{cm}^2\).
Total area:
\[
72 + 15 = 87 \, \text{cm}^2
\]
---
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 \(6 \, \text{cm} \times 10 \, \text{cm}\).
The total area is the sum of the areas of these rectangles:
- 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:
\[
300 + 60 = 360 \, \text{cm}^2
\]
---
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 \(4 \, \text{cm} \times 3 \, \text{cm}\).
However, the smaller rectangle is subtracted from the larger one because it is a cut-out section. The effective area is:
- 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:
\[
130 - 12 = 118 \, \text{cm}^2
\]
---
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 \(5 \, \text{cm} \times 2 \, \text{cm}\).
The total area is the sum of the areas of these rectangles:
- 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:
\[
27 + 8 + 10 = 45 \, \text{cm}^2
\]
---
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 \(2 \, \text{cm} \times 8 \, \text{cm}\).
The total area is the area of the large rectangle minus the areas of the three smaller rectangles:
- 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:
\[
480 - (48 + 48 + 16) = 480 - 112 = 368 \, \text{cm}^2
\]
---
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 \(3 \, \text{cm} \times 3 \, \text{cm}\).
The total area is the area of the large rectangle minus the areas of the two smaller rectangles:
- 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:
\[
56 - (6 + 9) = 56 - 15 = 41 \, \text{cm}^2
\]
---
Final Answers
\[
\boxed{87, 360, 118, 45, 368, 41}
\]
Parent Tip: Review the logic above to help your child master the concept of area of complex shapes worksheet.
