PERIMETER: Formula, and the Concept with Examples
NCERT Class 4th Maths
In today’s article, we are going to discuss an important concept of NCERT Class 4th Mathematics, i.e., Perimeter. Let’s dive in to know Perimeter formulas and its concept with examples.
INTRODUCTION TO PERIMETER:
The word Perimeter comes from two Greek words “PERI” which means around and “METER” which means measure. A Perimeter is used either to indicate the path or its length—in one dimension.
- The perimeter is the length of the outline of a shape.
- A Perimeter of any polygon is the total distance along the outside of the polygon.
- The perimeter of a circle or ellipse is known as its circumference.
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PERIMETER OF REGULAR SHAPES:
1. The perimeter of a Polygon: is the sum of the lengths of all the sides.
2. The perimeter of Rectangle:
The perimeter of a rectangle is found by adding up the length of all four sides.
If x is, in this case, the length of the rectangle while y is the width of the rectangle.
The perimeter, P, is:
P = x + x + y + y
P = 2x + 2y
P = 2 (x + y)
The formula for the perimeter of a rectangle is often written as P = 2l + 2w, where l is the length of the rectangle and w is the width of the rectangle.
Example – Consider a rectangle with two long sides are 12 cm, and the two shorter sides are 7 cm, the perimeter can be found by:12+12+7+7=38
The perimeter is 38 cm.
3. Perimeter of Square:
To find the perimeter of a square you have to add the lengths of all the four sides.
The perimeter of any closed geometrical object is defined as the distance around that object i.e. the length of its boundary. So, it can be said that a square’s perimeter is its total boundary. For a square, the perimeter is calculated by adding its four sides.
We know that all the sides of a square are equal and hence, its perimeter will be 4 times its side, i.e. 4 × sides.
The formula for Perimeter of a Square Perimeter of Square (P) = 4 × side
Derivation of a Square’s Perimeter
The perimeter of the square is defined as the length of the boundary of a square.
The Perimeter of the square formula is given by,
Perimeter = sum of the lengths of 4 sides
= side + side +side + side
= 4 × side
Therefore, the perimeter of Square = 4s units
Example – Find the perimeter of a square whose side is 5 cm?
Side, s = 5 cm
The formula to find the perimeter of a square is given by
The perimeter of Square = 4s units
Substitute the value of‘s’ in the perimeter formula,
P= 4 × 5 cm
P = 20 cm
Therefore, the perimeter of square = 20 cm
4. Perimeter of a Triangle:
An equilateral triangle is the one where all sides are equal and have an equal angle.
Perimeter of an Equilateral Triangle= 3a
where a is the side of an equilateral triangle.
Example – Find the area, altitude, perimeter, and semi-perimeter of an equilateral triangle whose side is 8 cm?
Side of an equilateral triangle = a = 8 cm
Perimeter of an equilateral triangle
= 3 × 8 cm
= 24 cm
5. Perimeter of A Rhombus:
When a Rhombus is concerned, it is a flat shape with four same sides and four angles that are NOT necessarily 90 degrees. A rhombus is often called as a diamond or diamond-shaped. The total distance traveled along the border of a rhombus is the perimeter of a rhombus.
In the case of a rhombus, all four sides are the same length by definition, so the perimeter is four times the length of a side. Or as a formula:
Perimeter of a Rhombus = 4s where s is the length of the side of rhombus.
Example: Find the perimeter of a rhombus having side as 5 cm?
a = 5 cm
Perimeter of a rhombus = 4 × a
Perimeter of a rhombus = 4 × 5
Perimeter of a rhombus = 20
6. Perimeter Of A Regular Pentagon:
A regular pentagon is a five-sided polygon.
All the five sides of a regular pentagon are equal.
Perimeter of Regular Pentagon is equal to five times the length its side.
Perimeter of Regular Pentagon = 5 x Length of each side
Example – Find the perimeter of a regular pentagon of side 3cm?
A regular pentagon is a five-sided polygon.
All five sides of a regular pentagon are equal.
So, Length of each side of regular pentagon = 3cm
Perimeter of regular pentagon = (5 x Length of each side) units
= (5 x 3) cm
= 15 cm
7. Perimeter of a Regular Hexagon:
In geometry, a hexagon is said to the polygon which has six equal sides and six edges. Hexa comes from Greek word “Hex” meaning “six” in English and “gonia” meaning angles. Naturally, the perimeter of the hexagon will be 6 multiplied by one side of the hexagon. Each internal angle of the hexagon is 120∘.
Formula of Perimeter of Hexagon:
Example : Find the perimeter of the hexagon with one side 12 cm?
a = 6 cm
Formula of hexagon perimeter,
P = 6 × a
P = 6 × 12
P = 72 cm
PERIMETER OF AN IRREGULAR SHAPE
A regular shape is a shape in which every side is the same length. If a shape is not regular then it is irregular.
An irregular shape is simply a shape where not every single side is the same length. If a shape is irregular then it has angles that are not all the same size. To find the perimeter of an irregular shape, we simply add up each of its outer sides.
For example, an irregular triangle has three sides and an irregular pentagon has five sides.
To find the perimeter of an irregular shape we add up all of the lengths of its outer sides.
Example – Find the perimeter of a quadrilateral with sides 14 cm, 12cm, 5cm and 5cm.
The two largest sides are 14 cm and 12 cm. These add together to make 26 cm.
The two remaining sides are 5 cm and 5 + 5 = 10, using number bonds.
26 cm + 10 cm = 36 cm
The perimeter of this irregular quadrilateral is 36 cm.
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