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103 LearnersLast updated on October 7, 2025
Perimeter of Combined Shapes
The perimeter of a shape is the total length of its boundary. When dealing with combined shapes, the perimeter is obtained by summing the lengths of all the outer sides. Perimeter calculations are essential in various practical applications such as fencing a property, sewing, and more. In this topic, we will explore the perimeter of combined shapes.
What is the Perimeter of Combined Shapes?
The perimeter of combined shapes involves summing the lengths of all outer sides. By adding together the lengths of all sides that form the outer boundary, we obtain the perimeter of the combined shape.
For instance, consider a shape formed by combining a rectangle and a semicircle.
If the rectangle has a length of 8 and a width of 4, and the semicircle has a diameter of 4, the perimeter includes the rectangle's perimeter minus the diameter, plus the semicircle's curved part.
Formula for Perimeter of Combined Shapes
Consider a shape formed by combining two rectangles. If the first rectangle has a length of 10 and width of 5, and the second rectangle has a length of 7 and width of 3, the perimeter would be:
Perimeter = (2×(10+5)) + (2×(7+3)) - 2×common length
This accounts for the shared side that doesn't contribute to the perimeter.
How to Calculate the Perimeter of Combined Shapes
To calculate the perimeter of combined shapes, apply the perimeter formulas for individual shapes, then adjust for shared or internal sides. For example, a shape combines a triangle with sides 6, 8, and 10, with a rectangle of length 6 and width 4.
The perimeter = sum of outer sides = 6 + 8 + 10 + 4 + 4.
Example Problem on Perimeter of Combined Shapes -
A combined shape consists of a square with side 5 and a semicircle with a diameter of 5.
The perimeter is calculated by: Perimeter = 4×5 + (π×(5/2)) - 5
Thus, the perimeter of the combined shape is approximately 30.7 units.
Tips and Tricks for Perimeter of Combined Shapes
Here are some helpful tips and tricks for calculating the perimeter of combined shapes:
1. Always remember to exclude any shared or internal sides in the calculation of the perimeter.
2. When dealing with curves like semicircles, calculate the perimeter of the curved portion separately and add it to the linear parts. Use the formula: Curved part of a semicircle = π×radius.
3. Arrange the indicated side lengths of each individual shape clearly when calculating the perimeter of a group of shapes.
4. Use precise and constant side lengths for practical applications like architecture and gardening to avoid errors.
5. If given the semi-perimeter in problems involving curves, remember it only pertains to the curved portion.
Common Mistakes and How to Avoid Them in Perimeter of Combined Shapes
While working with the perimeter of combined shapes, errors can occur. Here are solutions to common problems:
Mistake 1
Neglecting shared sides in combined shapes.
Ensure shared sides in combined shapes are not double-counted when calculating the perimeter.
Mistake 2
Confusing area with the perimeter, leading to incorrect calculations.
Remember, perimeter is measured in linear units, representing the total length of the outer sides, whereas area is in square units, covering the space inside the shape.
Mistake 3
Assuming all shapes contribute equally to the perimeter.
Different shapes have different contributions to the perimeter, especially if curves are involved. Calculate each part accurately.
Mistake 4
Using incorrect values for the lengths of sides due to misreading a problem.
Double-check the problem and ensure correct lengths are used for each shape.
Mistake 5
Misunderstanding or misidentifying which sides are part of the perimeter in combined shapes.
Carefully analyze the shape to determine which sides form the outer boundary.
Perimeter of Combined Shapes Examples
Problem 1
A garden is designed in the shape of an L, with a long side of 12 meters, a short side of 6 meters, and a width of 3 meters. Find the perimeter of the garden.
The perimeter of the garden is 36 meters.
Explanation
Consider the shape as two rectangles sharing a side: Perimeter = 12 + 6 + 3 + 3 + 6 + 6 = 36 meters.
Problem 2
A path is created by combining a square with side 5 and a quarter circle with radius 5. Calculate the total perimeter.
The total perimeter is approximately 26.57 units.
Explanation
Calculate the perimeter: Square = 4×5 = 20 Quarter circle = (π×5)/2
Total perimeter = 20 + 7.85 - 5 = 26.57
Problem 3
Find the perimeter of a rectangle with length 8 cm and width 6 cm, combined with a semicircle of diameter 6 cm.
The perimeter is approximately 37.42 cm.
Explanation
Rectangle's perimeter: 2×(8+6) = 28
Semicircle's curved part: (π×3) = 9.42
Total perimeter: 28 + 9.42 - 6 = 37.42 cm
Problem 4
Mia is creating a border around her flower bed, combining a triangle with sides 7, 9, and 11 meters with a rectangle of length 9 and width 3. What is the total perimeter?
The total perimeter is 41 meters.
Explanation
Calculate the perimeter: Triangle = 7 + 9 + 11 = 27
Rectangle = 2×(9+3) = 24
Subtract shared side: 24 - 9
Total perimeter = 27 + 15 = 41 meters
Problem 5
A playground has a shape formed by a rectangle of length 10 meters and width 5 meters, combined with a semicircle with a diameter of 5 meters. Find the perimeter.
The perimeter is approximately 38.57 meters.
Explanation
Calculate the perimeter: Rectangle = 2×(10+5) = 30
Semicircle's curved part = (π×2.5) = 7.85
Total perimeter = 30 + 7.85 - 5 = 38.57 meters
FAQs on Perimeter of Combined Shapes
1.Evaluate the perimeter of a shape combining a rectangle of 6 cm by 4 cm and a semicircle of diameter 4 cm.
2.What is meant by the perimeter of combined shapes?
3.What are some basic shapes used in forming combined shapes?
4.Which strategies help in calculating the perimeter of complex combined shapes?
5.How do you handle curves in combined shapes?
Important Glossaries for Perimeter of Combined Shapes
- Perimeter: The total length of the outer edges of a shape.
- Combined Shape: A shape formed by combining two or more basic geometric shapes.
- Semicircle: A half-circle, often contributing a curved part to a combined shape's perimeter.
- Shared Side: A side common to two shapes in a combined shape, often excluded in perimeter calculations.
- Curved Part: The non-linear portion of a shape's perimeter, such as an arc in a circle or semicircle.
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Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
