This topic gives an overview of;
We know that the value of an algebraic expression depends on the values of the variables forming the expression. There are a number of situations in which we need to find the value of an expression, such as when we wish to check whether a particular value of a variable satisfies a given equation or not.
We find values of expressions, also, when we use formulas from geometry and from everyday mathematics. For example, the area of a square is l^{2}, where l is the length of a side of the square. If l = 5 cm., the area is 5^{2} cm^{2} or 25 cm^{2} ; if the side is 10 cm, the area is 10^{2} cm^{2} or 100 cm^{2} and so on.
We have seen earlier also that formulas and rules in mathematics can be written in a concise and general form using algebraic expressions. We see below several examples.
Once a formula, that is, the algebraic expression for a given quantity is known, the value of the quantity can be computed as required.
For example, for a square of length 3 cm, the perimeter is obtained by putting the value l = 3 cm in the expression of the perimeter of a square, i.e., 4l. The perimeter of the given square = (4 × 3) cm = 12 cm.
Similarly, the area of the square is obtained by putting in the value of l(= 3 cm) in the expression for the area of a square, that is, l^{2} ; Area of the given square = (3)^{2} cm^{2} = 9 cm^{2} .
Study the following statements:
Let us now look at another pattern of numbers, this time without any drawing to help us 3, 6, 9, 12, ..., 3n, ...
The numbers are such that they are multiples of 3 arranged in an increasing order, beginning with 3. The term which occurs at the nth position is given by the expression 3n. You can easily find the term which occurs in the 10th position (which is 3 × 10 = 30); 100th position (which is 3 × 100 = 300) and so on.
What is the number of diagonals we can draw from one vertex of a quadrilateral? Check it, it is one From one vertex of a pentagon? Check it, it is 2.From one vertex of a hexagon? It is 3.
The number of diagonals we can draw from one vertex of a polygon of n sides is (n – 3). Check it for a heptagon (7 sides) and octagon (8 sides) by drawing figures. What is the number for a triangle (3 sides)? Observe that the diagonals drawn from any one vertex divide the polygon in as many non-overlapping triangles as the number of diagonals that can be drawn from the vertex plus one.
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