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Perimeter is a fundamental concept in geometry that refers to the total length of the boundary surrounding a two-dimensional shape. It’s an essential measure used in various fields, including architecture, engineering, and everyday problem-solving. Whether you’re fencing a yard, framing a picture, or designing a garden, understanding perimeter helps in determining how much material one needs to cover the edges.
Definition of Perimeter
The definition of perimeter is the total distance around its edge. In simple terms, it is the length of the outline or boundary of any two-dimensional geometric figure.
For example, imagine you have a square garden, and each side of the garden measures 5 meters.
To find the perimeter of the garden, you would add up the lengths of all four sides: 5 meters + 5 meters + 5 meters + 5 meters, resulting in a perimeter of 20 meters. This is the total distance you would travel if you walked around the garden once.
What is Perimeter?
Perimeter is the sum of all the sides of a shape, and it is expressed in linear units such as meters, feet, or inches. The unit of perimeter is meter. For different shapes, the method of calculating the perimeter can vary.
For example, the perimeter of a rectangle is calculated by adding the lengths of all four sides or by using the formula P = 2(l + b), where l is the length and b is the breadth.
How to Calculate Perimeter?
The outer boundary that makes up a geometrical shape is called its perimeter. To know how to find perimeter involves measuring the length of the sides of the shape and then summing them up. Here’s a step-by-step guide on how to calculate the perimeter, using a rectangular farm as an example:
Step 1: Understand the Shape
First, identify the shape of the object you are measuring. In this case, the farm is rectangular. A rectangle has four sides, with opposite sides being equal in length and all angles being 90 degrees.
Step 2: Label the Sides
Name the sides of the rectangle. Typically, the longer side is labeled as ‘l’ length, and the shorter side is labeled as ‘b’ breadth.
Step 3: Measure the Sides
Measure the length of both the longer side ‘l’ and the shorter side ‘b’. If the farm’s length is 50 meters and the breadth is 30 meters, these are the values you’ll use.
Step 4: Apply the Perimeter Formula
To find the perimeter of the rectangle, use the formula:
Perimeter = 2(l + b)
Substitute the values you have measured into the formula. For example, if l = 50 meters and b = 30 meters, the calculation will be:
Perimeter = 2(50 + 30) = 2*80 = 160 meters
Step 5: Interpret the Result
The result gives you the total distance around the rectangle, which in this case is 160 meters. This is the length of wire David would need to completely fence his farm.
Units of Perimeter
Perimeter is the total distance around the boundary of a two-dimensional shape, and it is measured in linear units. Common units for measuring perimeter include meters, centimeters, and millimeters in the metric system, and inches, feet, and yards in the imperial system. For larger distances, kilometers and miles are used.
Perimeter Formula for Different Shapes
Perimeter is calculated differently for various shapes, depending on the number of sides and their lengths. Below are the formulas for the perimeter of common geometric shapes, along with examples to illustrate each calculation.
1. Perimeter Formula of a Square
The perimeter of a square is calculated by adding up the lengths of all four equal sides. The formula is:
Perimeter = 4 side
Example:
If each side of a square garden is 10 meters, the perimeter would be:
Perimeter = 4 10 = 40 meters
This means that the total distance around the garden is 40 meters.
2. Perimeter Formula of a Rectangle
The perimeter of a rectangle is found by adding the lengths of all four sides, or by using the formula:
Perimeter = 2 (length + breadth)
Example:
For a rectangular field with a length of 15 meters and a breadth of 8 meters:
Perimeter = 2 times (15 + 8) = 2 times 23 = 46 meters
This indicates that the boundary of the field is 46 meters long.
3. Perimeter Formula of a Triangle
The perimeter of a triangle is the sum of the lengths of its three sides:
Perimeter = side_1 + side_2 + side_3
Example:
Consider a triangle with sides measuring 7 cm, 9 cm, and 12 cm:
Perimeter = 7 + 9 + 12 = 28 cm
The perimeter of the triangle is therefore 28 cm.
4. Perimeter Formula of a Parallelogram
The perimeter of a parallelogram is calculated by adding the lengths of its opposite sides, or by using:
Perimeter = 2 times (base + side)
Example:
For a parallelogram with a base of 12 cm and a side length of 7 cm:
Perimeter = 2 times (12 + 7) = 2 times 19 = 38 cm
Thus, the total perimeter is 38 cm.
5. Perimeter of a Rhombus
Since all sides of a rhombus are equal, the perimeter is:
Perimeter = 4 times side
Example:
If each side of a rhombus is 6 meters long, the perimeter would be:
Perimeter = 4 times 6 = 24 meters
The perimeter of the rhombus is therefore 24 meters.
6. Perimeter of an Equilateral Triangle
In an equilateral triangle, all three sides are equal, so the perimeter is:
Perimeter = 3 times side
Example:
For an equilateral triangle with each side measuring 5 cm:
Perimeter = 3 5 = 15 cm
The perimeter of the equilateral triangle is 15 cm.
7. Perimeter of a Circle (Circumference)
The perimeter of a circle, known as the circumference, is given by:
Perimeter = 2 r
where ( r ) is the radius of the circle.
Example:
If the radius of a circular park is 7 meters:
Perimeter = 2 r
= 2 3.14 7 = 43.96 meters
The circumference, or perimeter, of the circle is approximately 43.96 meters.
Difference Between Perimeter and Area
Perimeter and area are both essential concepts in geometry, but they measure different aspects of a shape. The perimeter measures the total distance around the boundary of a shape, while the area measures the space enclosed within that boundary. Understanding the distinction between these two concepts is crucial for solving various mathematical and practical problems.
| Perimeter | Area |
| The total length around the boundary of a shape. | The total space enclosed within the boundary of a shape. |
| Linear measurement (measured in units like meters, feet). | Square measurement (measured in square units like square meters, square feet). |
| Depends on the shape (e.g. P=4×side for a square). | Depends on the shape e.g A = (side)2 for a square. |
| Perimeter of a rectangle: P=2(length+breadth) | Area of a rectangle: A=length×breadthA = \text{length} \times \text{breadth}A=length×breadth. |
| One-dimensional (length). | Two-dimensional (length × breadth). |
| Used to measure the length of the boundary (e.g., fencing). | Used to measure the surface covered (e.g., flooring). |
FAQs on Perimeter
How to convert area to perimeter?
To convert area to perimeter, it's important to understand that area and perimeter are two distinct measurements that describe different properties of a shape. Area measures the space contained within a shape, while perimeter measures the total distance around that shape. Therefore, there is no direct conversion between area and perimeter without additional information about the shape in question. For example, if you know the area of a square, you can find its side length by taking the square root of the area, and then multiply that side length by four to find the perimeter. However, this method is specific to squares and does not apply universally to all shapes.
How to find length and perimeter?
Finding length and perimeter involves understanding the specific shape you are working with. For a rectangle, the length can be found by dividing the area by the width if the area is known. The perimeter can then be calculated using the formula P=2(l+w), where l is the length and w is the width. In the case of a circle, the length refers to the radius or diameter, and the perimeter, known as the circumference, can be calculated using the formula C=2πr or C=πd, where r is the radius and d is the diameter. Thus, the method of finding length and perimeter varies based on the geometric figure involved.
Is perimeter the same as length?
Perimeter is not the same as length, although the two terms are often used interchangeably in casual conversation. Length typically refers to the measurement of one dimension of an object, such as the length of a side of a rectangle or the radius of a circle. In contrast, perimeter refers to the total distance around a shape, which is the sum of all its sides. For example, a rectangle with a length of 5 units and a width of 3 units has a perimeter of 16 units, calculated as 2(5+3). Thus, while length can be a component of perimeter, they are fundamentally different concepts.
What is area and perimeter?
Area and perimeter are both essential concepts in geometry that describe different attributes of shapes. Area quantifies the amount of space a shape occupies and is measured in square units, such as square meters or square feet. Perimeter, on the other hand, measures the total distance around a shape and is expressed in linear units, such as meters or feet. Understanding both area and perimeter is crucial for various applications, including architecture, landscaping, and any field that involves spatial planning.
What does it mean by the perimeter?
The term perimeter refers to the total length of the boundary surrounding a two-dimensional shape. It is calculated by adding together the lengths of all the sides of the shape. For example, for a triangle, the perimeter is the sum of the lengths of its three sides, while for a rectangle, it is the sum of twice the length and twice the width. The concept of perimeter is important in real-life applications, such as determining the amount of fencing needed for a yard or the length of material required to border a garden. Understanding how to calculate perimeter helps in making informed decisions in various practical scenarios.
