# Area and Perimeter Formula

When you come across an algebraic expression, say 2x + 3, you will probably find it hard to find any relevance in the real-life context. But as you know, the beauty of algebra is the simplicity with which it expresses generality. Similarly, using the algebraic expressions you can generalize and derive a number of formulas and rules in mathematics in a concise manner. In this article, we will learn about two of them – the perimeter formula and the area formula.

### Perimeter Formula

A Perimeter is the length of the boundary of a closed geometrical figure. There is a set perimeter formula which simplifies your task of calculation. Algebraic expressions can be used to represent the perimeter formula for the regular polygons. Say that the length of each side of a regular polygon is l. The perimeter formula for each of the polygon can be given using the same variable l

Equilateral Triangle

• The perimeter of an equilateral triangle = 3 x length of a side = 3l.

Square

• Similarly, the perimeter of a square = 4l.

Regular Pentagon

• The perimeter of a regular pentagon = 5l.

You can represent the perimeter formula for regular polygons in the similar fashion. The perimeter of a regular polygon of N sides can be given of N x l

So the perimeter of any square of known side length, say 4 cm, can be calculated simply by using the algebraic expression 4×l = 4 x 4 = 16 cm.

### Area Formula

The area is the measurement of space enclosed by a closed geometrical figure. Like the perimeter formula, there is also a set of area formula for polygons that can be represented using algebraic expressions. Some of them are:

• Area of a square of side l = $l^{2}$.
• Area of a rectangle of length l and breadth b = l x blb.
• Area of a triangle of base b and height h = $\frac{bh}{2}$.

So the area of any square of known side length, say 5 cm, can be calculated simply by using the algebraic expression $l^{2}$< = 5 x 5 = 25 cm.

Area and Perimeter is a very important topic in math and students are advised to refer NCERT solutions for better understanding and preparation. BYJU’S brings you NCERT solutions for – Perimeter and Area

#### Practise This Question

In the given figure, AB || CD, then the value of x is