Perimeter
The total length of the boundary of a closed shape is called its perimeter. Let’s try and understand this using an example. For example, you have a huge farm, square in shape. Now, in order to save your farm from street animals, you decide to fence it. If you know the length of one side of the farm, you just have to multiply it by 4 in order to find the total perimeter of the farm. There are many such instances where we might be using the concepts of finding perimeter without even knowing about it. Let us have a look at the article in order to understand the concept in a better way.
| 1. | What is Perimeter? |
| 2. | How to Find Perimeter? |
| 3. | Perimeter Formula |
| 4. | Difference Between Area and Perimeter |
| 5. | FAQs on Perimeter |
What is Perimeter?
The perimeter of a shape is defined as the total distance around the shape. It is the length of any shape that can be expanded in a linear form. The perimeter of different figures can be equal in measure depending upon the dimensions. For example, imagine a triangle made of a wire of length L, the same wire can be reused to make a square, considering that all the sides are equal in length.
How to Find Perimeter?
The outer boundary that makes up a geometrical shape is called its perimeter. Now, how does one calculate the perimeter? Let us consider an example. David wants to put a fence around his farm so that his sheep will not wander away. He wants to know how much wire he would need to fence around his farm. The shape of his farm is rectangular, which means that:
- It has four sides
- The opposite sides are of equal length
- All angles are 90 degrees each
Let us first name the sides of his farm. The larger side of this rectangular farm is named l, and the smaller side is named b. Now, if we add the distance of all 4 sides of his farm, it will give us the perimeter. Total distance = l+b+l+b=2l+2b. Therefore, the perimeter of a rectangle = 2(l+b).
Perimeter Units
Perimeter is the measure of length covered by the boundary of the shape. Hence, the units of the perimeter will be the same as the units of length. Hence, the perimeter can be measured in meters, kilometers, centimeters, and so on. Some other common units of measuring the perimeter that accepted worldwide are inches, feet, yards, and miles.
Perimeter Formula
The total length of the boundary of a closed shape is called its perimeter. Imagine a square-shaped chocolate piece with a side length of 1 inch. The perimeter of any 2-dimensional figures is measured as the sum of all the sides. Hence, the perimeter of a given square-shaped chocolate piece is 1+1+1+1 = 4 inches. The perimeter formula is Perimeter = Sum of all the sides. The perimeter formula for different 2-D figures is shown in the table below:
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PERIMETER FORMULAS |
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| Square | The perimeter of a square = 4 × L L = length of a side. |
| The perimeter of a rectangle = 2 ×(p + q) p,q = length of adjacent sides |
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| The perimeter of a triangle = a + b + c a, b, c = lengths of sides |
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| The perimeter of a quadrilateral = a + b + c + d a, b, c, d = lengths of sides |
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| The perimeter of a circle = 2 π r r = radius |
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Difference Between Area and Perimeter
The area is the space occupied by shape whereas the perimeter is the total distance covered around the edge of the shape. We define area as the amount of space covered by a flat surface of a particular shape. It is measured in terms of the "number of" square units (square yards, square inches, square feet, etc.). Most objects or shapes have edges and corners. The length and breadth of these edges are considered while calculating the area of a specific shape. On the other hand, the perimeter is the measure of length covered by the boundary of the shape. First, have a look at the image given here to understand what area of any shape means:
We know that the area of a rectangle is 2(l + b); while the area of a rectangle is l × b. Similarly, the area of a square (as seen above) is a2, while the perimeter of that square is 4a. Let us have a look at the formulas for the area and perimeter of some of the common shapes:
| Area of square = side2 | Perimeter of square = 4 x side |
| Area of a rectangle = length × breadth | Perimeter of rectangle = 2(length+breadth) |
| Area of triangle = ½ × base × height | Perimeter of triangle = Sum of all three sides |
| Area of rhombus = ½ (product of diagonals) | Perimeter of rhombus = 4 × side |
| Area of trapezium = ½ (sum of parallel sides) | Perimeter of trapezium = sum of all sides |
Solved Examples on Perimeter
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Example 1: Your favorite chocolate bar is made up of equal-sized squares with each side of the square measuring 1 in. Calculate its perimeter.
Solution:
We know that each little square has all its sides = 1 in. If we count and add the sides of squares along the length of the bar, we get 3 in. The sides of squares along the breadth of the bar add up to 2 in. Therefore, the length of the bar = 3 in. The breadth of the bar = 2 in. ∴ The perimeter of the chocolate bar is 10 in.
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Example 2: Henry needs to put the carpet in his living room in square shape. If he knows the dimensions of the room, which formula shall he apply?
Solution:
If Henry needs a carpet for his room, then he needs to cover the whole space occupied by the floor. By definition, the measurement of space occupied by the carpet refers to its area. ∴ Henry needs to apply the formula for Area.
FAQs on Perimeter
What is the Perimeter in Feet?
Perimeter is the measure of the length of boundary covering a particular shape. Hence, it has the unit of length. For example, let us find the perimeter in feet of a square. Consider a square of a side 4 meters. The perimeter of a square is 4×(side). So, Perimeter = 4×4 = 16 m. Now, converting it into feet, we get 16 m = 16 × 3.28 ft = 52.5 ft.
What is the Perimeter of a Table?
Consider a rectangular table with length 30 in and breadth 25 in. Therefore, the length of the table = 30 in. The breadth of the table = 25 in. Perimeter = 2(l+b) = 2(30+25) = 2(55) = 110 in.
Where do we Use Perimeter in Real Life?
Perimeter is very useful in real life and plays a crucial role. If you are planning to construct a house then an accurate perimeter is required of doors, windows, roof, walls, etc.
What is the Formula for Perimeter?
The total length of the boundary of a closed shape is called its perimeter. Hence, the perimeter of that shape is measured as the sum of all the sides. Thus, the perimeter formula is Perimeter(P) = Sum of all the sides.
What is a Perimeter of a Shape?
The total length of the boundary of a closed shape is called its perimeter.
What is the Difference Between Area and Perimeter?
The area is the space occupied by shape whereas the perimeter is the total distance covered around the edge of the shape. For example, the area of a rectangle is 2(l + b); while the area of a rectangle is l × b. Similarly, the area of a square (as seen above) is a2, while the perimeter of the square is 4a.