Page 1 - 12.3-LN-Expressions with variables and use of expressions in real life

SAI International School
CLASS-VII

Mathematics
CHAPTER-12: Algebraic Expression
LESSON NOTES-12.3

SUBTOPIC: Expressions with variables and use of expressions in
real life

Using Algebraic Expressions – Formulas and Rules: Rules and
formulas in mathematics are written in a concise and general form using algebraic
expressions.

Perimeter Formula:
 Let l be the length of the side of an equilateral triangle.
So, Perimeter of equilateral triangle = 3 * Length of side of equilateral triangle = 3l
 Let l be the length of the side of a square.
So, Perimeter of equilateral triangle = 4 * Length of side of square = 4l
 Let l be the length of the side of a regular pentagon.
So, Perimeter of equilateral triangle = 5 * Length of side of regular pentagon = 5l
Area formula:
2
 If we denote the length of a square by l, then the area of the square = l
 If we denote the length of a rectangle by l and its breadth by b, then the area
of the rectangle = l * b = lb

 If b stands for the base and h for the height of a triangle, then the area of the

triangle = =

Rules for number patterns:
 If a natural number is denoted by n, its successor is (n + 1).
Ex: If n = 20, its successor is n + 1 = 21, which is known.
 If a natural number is denoted by n, 2n is an even number and (2n + 1) an
odd number.
Ex: Let n = 7; 2n = 2 * n = 2 * 7 = 14 is indeed an even number and
2n + 1 = 2 * 7 + 1 = 14 + 1 = 15 is indeed an odd number.
Pattern in geometry:
 The number of diagonals we can draw from one vertex to another of a
quadrilateral is 1.
 The number of diagonals we can draw from one vertex to another of a
pentagon is 2.
 The number of diagonals we can draw from one vertex to another of a
hexagon is 3.