Subscribe to our ▶️YouTube channel🔴 for the latest videos, updates, and tips.
Home | About Us | Contact Us | Privacy | Math Blog
Perimeter of a Figure
Perimeter of a figure is explained here.
Perimeter is the total length of the boundary of a closed figure.
We know that the total length of the boundary of a plane closed figure is called its perimeter. We can find the perimeter of a closed figure drawn on a square sheet by adding the length of unit squares along each side of the figure. The unit of perimeter is same as the unit of length.
The perimeter of a simple closed figure is the sum of the measures of line-segments which have surrounded the figure.
Perimeter of ∆ABC = length (AB + BC + CA)
Perimeter of the quadrilateral DEKN = length (DE + EK + KN + ND)
Perimeter of the hexagon PQRSTU = length (PQ + QR + RS + ST + TU + UP)
The perimeter of a circle is the measure of its circumference. The perimeter of the circle of center O is its circumference.
A farmer wishes to fence his field using barbed wire. To do so he wants to know how many meters of barbed wire he should buy. Can you help him?
Obviously, to know the length of the wire needed to fence the field, he should add the lengths of the four sides of the field.
25 m + 10 m + 21 m + 30 m = 86 m
Thus, the farmer should buy 86 m of barbed wire to fence his field. We see that the distance around the field gives the length of the barbed wire.
Such a distance around a figure is called the perimeter of the figure.
The distance accord the edge of a figure is its perimeter. It is the total length of the sides of a closed figure.
Note: The unit of perimeter is the same as the unit of the sides of the given polygon.
For example, if the sides of a polygon are given in centimeters, then the perimeter of the polygon will also be in centimeters.
Let us draw a closed figure PQRS on a square sheet as shown below. If we make a path along its boundary starting from point P, then the total length of the path will be equal to the sum of all the sides of the figure PQRS.
Here, the length of the path is = PQ + QR + RS + SP.
We can find the length of each line segment by counting the number of unit squares. Therefore, the total length of the path = 3 + 6 + 3 + 3 = 18 unit squares.
The total length of the boundary of a plane figure is called its perimeter. The unit of perimeter is the same as the unit of length of the sides of the figure.
For example:
Find the perimeter of the following figures drawn on the 1 cm square graph sheet.
|
Figure (i) AB = 3 cm BC = 2 cm CD = 3 cm DA = 2 cm AB + BC + CD + DA = 3 + 2 + 3 + 2 = 10 cm Perimeter of figure 1 = 10 cm |
Figure (ii) PQ = 1 cm QR = 2 cm RS = 1 cm ST = 2 cm TU = 1 cm UV = 2 cm VW = 1 cm WP = 6 cm PQ + QR + RS + ST + TU + UV + VW + WP = 1 + 2 + 1 + 2 + 1 + 2 + 1 + 6 = 16 cm Perimeter of figure 2 = 16 cm |
Look at the given figures. Find the length of the boundary of each of these simple closed figures made of line segments.
Length of the boundary of each figure is the sum of the lengths of its line segments.
Length of the boundary of each figure (a) is AB + BC + CA
= 4 cm + 4 cm + 4 cm
= 12 cm
Length of the boundary of each figure (b) = 4 cm + 3 cm + 4 cm + 3 cm
= 14 cm
Length of the boundary of each figure (c) = 3 cm + 3 cm + 3 cm + 3 cm
= 12 cm
The length of the boundary of a closed figure is called the perimeter of the figure.
1. Find the perimeter of the given triangle ABC.
In triangle ABC.
AB = 3 cm,
BC = 4 cm and
AC = 5 cm
The perimeter of the triangle = AB + BC + AC
= 3 + 4 + 5
= 12 cm.
2. Find the perimeter of the rectangle ABCD.
In rectangle ABCD,
AD = BC = 2 cm and
AB = DC = 4 cm
The perimeter of the rectangle ABCD will be the sum of the sides AB, BC, CD and AD.
So, the perimeter of rectangle ABCD
= AB + BC + CD + AD
= 4 cm + 2 cm + 4 cm + 2 cm
= 2(4 + 2) cm
= 2 (6) cm
= 2 × 6 cm
= 12 cm
The perimeter of rectangle ABCD
= length + breadth + length + breadth
= 2 times length + 2 times breadth
= 2 (length + breadth)
Perimeter of a rectangle = 2(length + breadth)
3. Find the perimeter of the square PQRS.
The perimeter of the square PQRS
= PQ + QR + RS + PS
= (2 + 2 + 2 + 2) cm
= 8 cm
Perimeter of a square = 4 x side of a square
Word Problems on Perimeter of a Figure
1. Three sides of a triangle are 3 cm, 5 cm and 4 cm. Find its perimeter.
Solution:
Perimeter of the given triangle
= sum of the sides
= 3 cm + 5 cm + 4 cm
= 12 cm
2. The length of a rectangle is 8 cm and its breadth is 5 cm. Find its perimeter.
Solution:
Length of the rectangle = 8 cm
Breadth of the rectangle = 5 cm
Perimeter of the rectangle = 2 (8 + 5) cm
= 2 × 13 cm
= 26 cm
3. The side of a square is 8 cm. Find its perimeter.
Solution:
The side of the square = 8 cm
Perimeter of the square = 4 × 8 = 32 cm
4. The length of a rectangle is 10 cm and its perimeter is 30 cm. Find its breadth.
Solution:
Length of the rectangle = 10 cm
Perimeter of the rectangle = 30 cm
Let us represent length as ℓ and breadth as b.
Now perimeter of the rectangle = 2 (ℓ + b)
or, 2 (ℓ + b) = 30 cm
or, 2(10 cm + b) = 30 cm
or, 20 cm + 2b = 30 cm
or, 2b = 30 cm - 20 cm
or, 2b = 10 cm
or, b = \(\frac{10}{2}\) cm
or, b = 5 cm
Therefore, breadth = 5 cm.
5. Ken walks around a playground in his daily morning walk. How far does he walk every morning? The playground is of the shape of a quadrilateral having sides of length 112 m, 85 m, 69 m and 102 m.
Solution:
Perimeter of the playground
= 112 m + 85 m + 69 m + 102 m
= 368m
Ken walks 368 m around the playground, i.e. around the perimeter, every morning.
Definition of Perimeter:
The total length of the boundary of a closed figure is called its perimeter.
Worksheet on Perimeter of a Figure
Now, answer the following questions to have a quick review of what we have learnt so far.
1. Fill in the blanks:
(i) …………………….. is the length of the boundary of a plane closed shape.
(ii) The perimeter of a square with side = 10 unit will be ……………………..
Answers:
(i) Perimeter
(ii) 40 units
2. Find the perimeter of the given figure if length of each square is 1 centimetre (cm).
(i) Perimeter =
(ii) Perimeter =
(iii) Perimeter =
(iv) Perimeter =
Answers:
(i) 30 cm
(ii) 42 cm
(iii) 24 cm
(iv) 26 cm
3. Find the perimeter of the given figures.
(i)
(ii)
(iii)
(iv)
(v)
Answers:
(i) 31 cm
(ii) 26 cm
(iii) 40 cm
(iv) 28 cm
(v) 19 cm
You might like these
Worksheet on Construction of Triangles | Constructing Triangles | Math
In worksheet on construction of triangles we will solve different types of questions. 1. Construct a triangle ABC in which BC = 6 cm, CA = 5 cm and AB = 4 cm.
Line Symmetry | Vertical & Horizontal Lines of Symmetry | Symmetrical
Line symmetry is discussed here. We know that any object or shape which can be cut in two equal halves in such a way that both the parts are exactly the same is called symmetrical and the line which divides the shape in two equal halves is called the line of symmetry.
Symmetrical Shapes | One, Two, Three, Four & Many-line Symmetry
Symmetrical shapes are discussed here in this topic. Any object or shape which can be cut in two equal halves in such a way that both the parts are exactly the same is called symmetrical. The line which divides the shape is called the symmetry. So, if we place a mirror
Constructing a Line Segment |Construction of Line Segment|Constructing
We will discuss here about constructing a line segment. We know how to draw a line segment of a certain length. Suppose we want to draw a line segment of 4.5 cm length.
Measuring the Line Segment | Comparing Line Segments
We will discuss here about measuring the line segment i.e. how to draw and measure a line segment using scale or ruler. We can measure a line segment by two ways. (i) With the help of scale
Simple Closed Curves | Types of Closed Curves | Collection of Curves
In simple closed curves the shapes are closed by line-segments or by a curved line. Triangle, quadrilateral, circle, etc., are examples of closed curves.
Worksheet on Line Symmetry | Geometry Worksheet | Line of Symmetry
Worksheet on line symmetry we will solve different types of questions. 4th grade students can practice this geometry worksheet to get the basic ideas on line symmetry. Fill in the blanks: (i) A square has …... lines of symmetry. (ii) An equilateral triangle has
Different Types of Polygons | Triangle, Quadrilateral|Pentagon|Hexagon
The different types of polygons are discussed here. In any polygon a pair of sides that are inclined to each other meet at a point. This point is called a vertex of the polygon. In the polygon there
What is a Quadrilateral? | Symbol of a Quadrilateral □ | Rectangle
What is a quadrilateral? A simple closed curve or a polygon formed by four line-segments is called a quadrilateral.
Classification of Angles | Types of Angles | Acute, Right, Obtuse, ...
Classification of angles on the basis of their degree measures are given below: Acute angle: An angle whose measure is more than 0° but less than 90° is called an acute angle. Angles having mag
Measuring an Angle | Using Protractor | Comparison of Angles | Example
We will discuss here about measuring an angle with the help of a protractor. You can find it in your Geometry Box. It has the semi-circular shape. Its semi-circular edge is divided
Comparing Different Line Segments | Difference of two line segments
We will discuss here about comparing different line segments. Different line segments can be of different lengths. We can compare the lengths of the different line segments
Circle Math | Parts of a Circle | Terms Related to the Circle | Symbol
In circle math the terms related to the circle are discussed here. A circle is such a closed curve whose every point is equidistant from a fixed point called its centre. The symbol of circle is O. We have learned to draw a circle, by tracing the outlines of objects like a
What is a Triangle? | Types of Triangle | Scalene Triangle | Isosceles
A simple closed curve or a polygon formed by three line-segments (sides) is called a triangle. The above shown shapes are triangles. The symbol of a triangle is ∆. A triangle is a polygon with three sides. In the given figure ABC is a triangle. AB, BC and CA are its sides.
What is a Polygon? | Simple Closed Curve | Triangle | Quadrilateral
What is a polygon? A simple closed curve made of three or more line-segments is called a polygon. A polygon has at least three line-segments.
● Related Concepts
● To Measure the Length of a Line-segment
● Examples on Unit of Mass or Weight
● Units for The Measurement of Capacity
● Examples on Measurement of Capacity
● Antemeridian (a.m.) or Postmeridian (p.m.)
● Calendar
● Reading and Interpreting a Calendar
4th Grade Math Activities
From Perimeter of a Figure to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Recent Articles
-
Formation of Square and Rectangle | Construction of Square & Rectangle
Jul 16, 25 02:45 AM
In formation of square and rectangle we will learn how to construct square and rectangle. Construction of a Square: We follow the method given below. Step I: We draw a line segment AB of the required… -
Perimeter of a Figure | Perimeter of a Simple Closed Figure | Examples
Jul 16, 25 02:33 AM
Perimeter of a figure is explained here. Perimeter is the total length of the boundary of a closed figure. The perimeter of a simple closed figure is the sum of the measures of line-segments which hav… -
Formation of Numbers | Smallest and Greatest Number| Number Formation
Jul 15, 25 11:46 AM
In formation of numbers we will learn the numbers having different numbers of digits. We know that: (i) Greatest number of one digit = 9, -
5th Grade Quadrilaterals | Square | Rectangle | Parallelogram |Rhombus
Jul 15, 25 02:01 AM
Quadrilaterals are known as four sided polygon.What is a quadrilateral? A closed figure made of our line segments is called a quadrilateral. For example: -
5th Grade Geometry Practice Test | Angle | Triangle | Circle |Free Ans
Jul 14, 25 01:53 AM
In 5th grade geometry practice test you will get different types of practice questions on lines, types of angle, triangles, properties of triangles, classification of triangles, construction of triang…
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.