Let us start with examples.
Consider a Square.
This is a square of side 1m.
Look at the shaded part inside the square.
The area of the square is 1 square unit.
That means, 1 square unit is needed to cover the surface enclosed by the square.
Now, consider a rectangle.
Its length is 3m and width is 2m.
There are 6 small squares contained in this.
Each small square is 1 sq m
This rectangle of length 3m and width 2m is 6 sq m in area.
Now, we state the above two examples in other way.
Area of the square is got by multiplying the side by itself.
If the side of the square is “s”, and the area is “A”, then
A = s × s
Here,
“s” and “A” are the symbols (Variables)
A = s × s is the relation
Also, area of the rectangle is obtained by multiplying the length and width.
If we represent the length as “L”, width as “W” and the area as “A”, then
A = L × W
Here,
“L”, “W” and “A” are the symbols (Variables)
A = L × W is the relation
We call the above two relations as the formula.
Hence,
A = s × s is the required formula to find the area of a square and
A = L × W is the required formula to find the area of a rectangle.
Thus,
The relation between two or more variables is called a formula.
In other words,
A formula is an equation that involves two or more variables that have a specific relationship with each other.
More Examples:
Consider the figure.
This is a solid.
Its length is 2m, width is 2m and height is 2m.
A solid whose length, width and height are equal is called a cube.
Volume is the quantity of matter contained in a solid.
Hence the volume is 2m × 2m × 2m = 8 cubic meters
Now, consider another solid.
This solid has length, width and height are different.
Such a solid is called a cuboid.
The volume of a cuboid is 1m × 4m × 3m = 12 cubic meters
Thus we have,
Cube = side × side × side,
Cuboid = Length × width × height
If a side of cube is “s” and the volume is “V”, then
V = s × s × s
If the length of cuboid is “L”, width is “W”, height is “H”, and the volume is “V”, then
V = L × W × H
Framing Formulae:
1) The perimeter of the rectangle is twice the sum of its length and width.
Let us write Perimeter as “P”, Length as “L” and width as “W”
Then, P = 2 (L + W)
This is how we frame the formula
2) The area of a triangle is the product of its base and height divided by 2.
If the area of the triangle is “A”, base is “B”, and the height is “H”, then
A = (B × H) / 2
3) The circumference of a circle is twice the product of pi and its radius
If we represent the circumference of circle as “C”, and radius as “r”, then
C = 2 ? r
4) The area of a parallelogram is the product of its base and height.
Let the area of a parallelogram be represented by the variable “A”, base by “B”, and height by “H”.
Then, A = B × H
5) Perimeter of a square is four times its side
Suppose perimeter is denoted as “P”, and side as “s”…
Then, P = 4 × s
Uses of Formulae:
Formulae are used to figure out the answers in a quicker way.
Example 1:
A water tank is of length 120cm, width 100cm and height 80cm.
What is the Volume of the tank?
Solution:
We are asked to find the volume of tank for the given length, width and height.
The Tank is in the shape of a cuboid.
For finding the answer, we make use of the formula.
V = L × W × H
V = 120cm x 100cm x 80cm
V = 960000 cubic cm
Example 2:
A park is of length 250 meters and width 220 meters.
What is the perimeter of the park?
Solution:
Here, we need to find the perimeter of the park.
The park is in the shape of rectangle.
So, the answer can be found easily by using the formula.
P = 2 (L + W)
P = 2 (250m + 220m)
P = 2 (470m)
P = 940m
Related Tags
Introduction to Formulae , Notes on Formulae , Explain Formulae