## What is Perimeter?

The perimeter refers to the total length of the sides or edges of a polygon, a two-dimensional figure with angles. When describing the measurement around a circle, we use the word circumference, which is simply the perimeter of a circle.

There are many practical applications for finding the perimeter of an object. Knowing how to find the perimeter is useful for finding the length of fence needed to surround a yard or garden, or the amount of decorative border to buy to cover the top edges of a room’s walls. Also, knowing the perimeter, or circumference, of a wheel will let you know how far it will roll through one revolution which can be used to tell the speed of a moving vehicle.

## Terms Used

The perimeter of a polygon is simply calculated by the taking the sum of each edge. There are some formulas that help is calculate the perimeter quickly.

We’ll represent the perimeter, the value we’re trying to find, with a capital P. For a shape that has all of its sides the same length, we’ll use an s to represent a side. We can also use s with a number after it to represent sides of shapes that have more or less than four sides, which may be the same or different lengths. We can write these variables like this: s1, s2, s3, etc.

For a shape that has two of its opposite sides the same as each other and its other two opposite sides the same as each other but different from the first two sides, we’ll need two variables. We’ll call the longer of the two distances ‘length’ and the shorter of the two distances ‘width.’ We’ll represent length with an l and width with a w, as follows:

• l = length
• w = width

## Perimeter of some well known figures

### Rectangle

A rectangle is a four-sided shape whose corners are all ninety degree angles. Each side of a rectangle is the same length as the one opposite to it.Thus the perimeter of the rectangle equals l+b+l+b= 2(l+b).

A rectangle has right angles like a square does, but it has two longer sides that are the same (length) and two shorter sides that are the same (width). If we know the length of one side and the width of another, we can add them together and multiply by 2. We write the formula this way: P = 2(l + w).

To find the perimeter of the rectangle shown here, we need to have the length of one of the longer sides and the width of one of the shorter sides. We see from the labels that the length is 6 and the width is 3.

Starting with our formula, P = 2(l + w), we then substitute 6 for the l and 3 for the w: P = 2(6 + 3). Adding 6 and 3 equals 9, so our equation now looks P = 2(9). Multiplying 2 times 9 gives us 18, which is the perimeter of the rectangle.

Perimeter and Area of Rectangle:

● The perimeter of rectangle = 2(l + b).

● Area of rectangle = l × b; (l and b are the length and breadth of rectangle)

● Diagonal of rectangle = √(l² + b²)

### Square

A square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles). It can also be defined as a rectangle in which two adjacent sides have equal length.

Each side of a square has the same length, so we can use our abbreviation s to represent a side. A square has four sides, so we can find its perimeter by finding the length of any side and multiplying it by 4. We write the formula this way: P = 4s.

In the picture shown here, each side of the square has a length of 6 feet. Using our formula, P = 4s, we plug in the value of the length of one side for s: P = 4 * 6 ft. 6 * 4 = 24, so the perimeter of our square is 24 feet.

Perimeter and Area of the Square:

● Perimeter of square = 4 × S.

● Area of square = S × S.

● Diagonal of square = S√2; (S is the side of square)

### Triangle

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane. In other words, there is only one plane that contains that triangle, and every triangle is contained in some plane.

Perimeter and Area of the Triangle:

● Perimeter of triangle = (a + b + c); (a, b, c are 3 sides of a triangle)

● Area of triangle = √(s(s – a) (s – b) (s – c)); (s is the semi-perimeter of triangle)

● S = 1/2 (a + b + c)

● Area of triangle = 1/2 × b × h; (b base , h height)

● Area of an equilateral triangle = (a²√3)/4; (a is the side of triangle)

### Parallelogram

a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

Perimeter and Area of the Parallelogram:

● Perimeter of parallelogram = 2 (sum of adjacent sides)

● Area of parallelogram = base × height

### Rhombus

A rhombus  is a simple (non-self-intersecting) quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length. The rhombus is often called a diamond. Every rhombus is a parallelogram and a kite. A rhombus with right angles is a square.

Perimeter and Area of the Rhombus:

● Area of rhombus = base × height

● Area of rhombus = 1/2 × length of one diagonal × length of other diagonal

● Perimeter of rhombus = 4 × side

### Trapezium

In Euclidean geometry, a quadrilateral with at least one pair of parallel sides is referred to as a trapezoid or trapezium. The parallel sides are called the bases of the trapezoid and the other two sides are called the legs or the lateral sides

Perimeter and Area of the Trapezium:

● Area of trapezium = 1/2 (sum of parallel sides) × (perpendicular distance between them)
= 1/2 (p₁ + p₂) × h (p₁, p₂ are 2 parallel sides)

### Circle

A Circle is a simple closed shape. It is the set of all points in a plane that are at a given distance from a given point, Also it can be defined as it is the curve traced out by a point that moves so that its distance from a given point is constant.

Circumference and Area of Circle:

● Circumference of circle = 2πr
= πd
Where, π = 3.14 or π = 22/7
r is the radius of circle
d is the diameter of circle
● Area of circle = πr²

● Area of ring = Area of outer circle – Area of inner circle.

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