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102 LearnersLast updated on September 26, 2025
Perimeter of Objects
The perimeter of an object is the total length of its boundary. For instance, the perimeter of a triangle is the sum of all its three sides. Perimeter calculations are essential for various practical applications including fencing properties, sewing, and more. In this topic, we will explore the perimeter of different objects.
What is the Perimeter of an Object?
The perimeter of an object is the total length around its boundary. For example, the perimeter of a triangle is found by adding the lengths of all three sides.
The general formula for the perimeter of a triangle is P = a + b + c , where a , b , and c are the sides of the triangle.
For example, if a triangle has sides a = 5 , b = 7 , and c = 9 , then its perimeter is P = 5 + 7 + 9 = 21 .
Formula for Perimeter of an Object
Let’s consider another example of a rectangle with a length of 10 units and a width of 6 units. The formula for the perimeter of a rectangle is P = 2(l + w)
. So, the perimeter of the rectangle will be: P = 2(10 + 6) = 2 x 16 = 32 units.
How to Calculate the Perimeter of Different Shapes
To find the perimeter of different shapes, we apply the appropriate formula and sum all the sides.
For instance, in a square, if each side measures 4 units, the perimeter = 4 x 4 = 16 units. Example Problem on Perimeter of a Square - Use the formula, P = 4 x side.
For example, let’s say the side length is 3 units. Now, the perimeter = 4 x 3 = 12 units. Therefore, the perimeter of the square is 12 units.
Tips and Tricks for Finding Perimeter
Learning some tips and tricks makes it easier for students to calculate the perimeter of various shapes. Here are some tips and tricks:
- Always remember that the perimeter is simply the sum of the side lengths of a shape.
- Use the appropriate formula for each shape, such as P = 4 x side for a square or P = 2(l + w) for a rectangle.
- When calculating the perimeter of polygons, start by determining the length of each side. For more complex shapes, divide them into known shapes whose perimeters can be calculated.
- To avoid mistakes when adding the perimeter, ensure the side lengths are precise and consistent, especially in practical applications like gardening and architecture.
- If you are given the semi-perimeter, which is half the perimeter, you can multiply it by 2 to determine the full perimeter.
Common Mistakes and How to Avoid Them in Perimeter Calculations
Did you know that while working with the perimeter of objects, students might encounter some errors or difficulties? Here are some solutions to resolve these problems:
Mistake 1
Confusing area with perimeter calculations.
Remember, the perimeter is calculated in linear units as the total length around a shape, while the area is in square units representing the space within a shape.
Mistake 2
Using incorrect formulas for different shapes.
Each shape has its specific formula for perimeter calculation. Ensure you are using the correct one, like \( P = 2(l + w) \) for rectangles and \( P = 4 \times \text{side} \) for squares.
Mistake 3
Misreading the problem or mislabeling the sides.
Double-check the problem to ensure you use the correct side lengths for your calculations. Draw diagrams if necessary to visualize the problem.
Mistake 4
Assuming all shapes are regular, leading to incorrect calculations.
Shapes like scalene triangles or irregular polygons have sides of different lengths. Always check the type of shape to ensure accurate calculations.
Perimeter Examples
Problem 1
A rectangular garden has a perimeter of 64 meters. If the length of the garden is 20 meters, what is the width?
The width of the garden is 12 meters.
Explanation
Let \( w \) be the width of the garden. Given perimeter P = 64 meters and length l = 20 meters.
Perimeter of rectangle = 2(l + w) .
64 = 2(20 + w) .
64 = 40 + 2w
24 = 2w
w = 12
Therefore, the width of the garden is 12 meters.
Problem 2
A metal wire of length 150 cm is bent to form a square. What is the length of each side of the square?
The length of each side of the square is 37.5 cm.
Explanation
Given the total length of the wire = Perimeter of the square = 150 cm.
Perimeter of a square = 4 x side.
150 = 4 x side
side = 150/4 = 37.5 cm.
Therefore, each side of the square is 37.5 cm.
Problem 3
Find the perimeter of a regular hexagon with side length 8 cm.
48 cm
Explanation
Perimeter of a regular hexagon = 6 x side.
P = 6 x 8 = 48 cm.
Therefore, the perimeter of the hexagon is 48 cm.
Problem 4
A triangle has sides measuring 7 cm, 10 cm, and 12 cm. Calculate its perimeter.
The perimeter of the triangle is 29 cm.
Explanation
The perimeter of a triangle is the sum of all three sides. Using the formula: P = a + b + c . P = 7 + 10 + 12 = 29 cm.
Problem 5
A pentagon-shaped park has equal side lengths of 15 meters. What is the perimeter of the park?
The perimeter of the park is 75 meters.
Explanation
Perimeter of a regular pentagon = 5 x side.
P = 5 x 15 = 75 meters.
Therefore, the perimeter of the park is 75 meters.
FAQs on Perimeter of Objects
1.How do you find the perimeter of a rectangle with sides 5 cm and 10 cm?
2.What is a perimeter in geometry?
3.What are some common shapes and their perimeter formulas?
4.What is the perimeter of a circle called?
5.Can perimeter be measured in square units?
Important Glossaries for Perimeter of Objects
- Perimeter: The total length of the boundary of a shape.
- Rectangle: A quadrilateral with opposite sides equal.
- Square: A quadrilateral with all sides equal and angles at 90 degrees.
- Hexagon: A polygon with six sides.
- Circumference: The perimeter of a circle.
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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
