Area and Perimeter
Category : 4th Class
LEARNING OBJECTIVES
This lesson will help you to:—
Real Life Examples
QUICK CONCEPT REVIEW
Diagrams/pictures
Perimeter
The perimeter of fig. 1 is the total distance around it.
The total distance around the fig. 1
= 3m + 2m + 2m + 3m + 2m + 5m = 17m
\[\therefore \]Perimeter of fig. 1 = 17 m.
Hence, the sum of all the lengths of shape is called its perimeter.
Here, each square is of side 1 unit.
Perimeter of shaded region
= 2 units + 5 units + 4 units + 2 units + 2 units
+ 3 units = 18 units
Perimeter of square in fig. 3
= Sum of the sides of the square
= 3m + 3m + 3m + 3m or
\[=4\times 3m=12m\]
Thus, perimeter of a square = 4 x side
Perimeter of a rectangle is the sum of the length of its sides.
Perimeter of rectangle in fig. 4
= sum of the sides of the rectangle
\[=3m+10m+3m+10m\]or
\[=(3m+3m)+(10m+10m)\]
\[=(2\times 3m)+(2\times 10m)\]
\[=2\times (3m+10m)\]
\[=2\times (13m)=26\text{ }m\]
Thus, perimeter of a rectangle = 2 x (length + width)
Perimeter of a circle is the distance around the circle.
Also, perimeter of a circle is known as circumference of it.
Amazing Facts
Historical Preview
AREA
Area is the total number of square units that fill a given shape.
Area of fig. 6
= Total number of squares in the shape
= 26 square units.
When we divide a square into squares of length 1 unit, then we can see that we get same number of squares in rows and columns.
In this case, we can multiply the number of squares in any one row with the number of squares in any one column to get the area of the square.
In fig. 7,
Area of square = (Number of squares in row) x (Number of squares in column)
\[=4\times 4=16\]square units
Thus, area of a square = side\[\times \]side.
When we divide a rectangle in squares of length 1 unit, then we can see that we get more number of squares in either rows or columns. In this case, we can multiply the number of squares in any one row with the number of squares in any one column to get the area of the rectangle.
In fig. 8, the area of rectangle
= (Number of squares in one row)
\[\times \](Number of squares in one column)
\[=7\times 5=\]35 square units
Thus, we have area of rectangle = length x breadth (width)
Note: We can use the formula to measure the area of triangle\[\text{=}\frac{\text{1}}{\text{2}}\text{ }\!\!\times\!\!\text{ base }\!\!\times\!\!\text{ height}\].
Examples
Suresh bought a mat as given below. He wants to know whether he can spread that mat in his living room.
Let us find the area of the mat.
The mat is divided into squares of length 1m. So, we get 4 squares in each row and 2 squares in each column.
\[\therefore \]The area of mat \[=4\times 2=8\]square metre
Sangeeta aunty bought a new saree for her nephew's wedding. She want to stitch a new matching lace around its boundary.
To find the length of the lace required to stitch around the boundary of the saree, we need to find its perimeter.
Perimeter of saree = 5m + 2m + 5m + 2m = 14 m
Thus, 14m lace is required for the saree.
Shortcut to problem solving
Perimeter of a square
\[=4\times \text{side}\]
Perimeter of rectangle
= 3 (length + breadth).
Perimeter of a triangle
= a + b + c.
where a, b, c are the sides of the triangle.
Area of a square
= side\[\times \]side
Area of rectangle
=Length\[\times \]breadth.
Area of a triangle
\[\text{=}\frac{\text{1}}{\text{2}}\text{ }\!\!\times\!\!\text{ base }\!\!\times\!\!\text{ height}\]
Misconcept/Concept
Misconcept: When a unit square is removed from a given shape then both its area and perimeter get reduced by square unit and a unit respectively.
Concept: When a unit square is removed from a given shape then its area gets reduced by a square unit but its perimeter either remains same or gets increased by few units.
Note: Example for the concept is elaborated for you after flow chart.
For example: Consider the square given below divided into unit squares.
Perimeter = 5 + 5 + 5 + 5
= 20 units
Area \[=5\times 5=25\]square units.
(i) Let us now remove a square unit from it and then calculate the area and perimeter of the whole square.
Perimeter = 5 + 5 + 5 + 2 + 1 + 1 + 1 + 2
= 22 units
Area = 24 square units.
(ii) Let us now remove a square unit from the corner and then calculated the area and perimeter of the whole square.
Perimeter = 4 + 1 + 1 + 4 + 5 + 5
= 20 units
Area = 24 square units.
Thus, we can see that when we remove unit square from a shape then its area gets reduced by a square unit and its perimeter either remains the same or gets increased by few units.
You need to login to perform this action.
You will be redirected in
3 sec