## Area, Perimeter formula

Mathematically, area and perimeter form the two principal formulas for any two-dimensional shape. Among the shapes you will see in geometry are circles, triangles, squares, pentagons, octagons, etc. Each shape has its own properties dependent on its structure, sides, and angles. The area and perimeter are the two most important features. Geometric shapes all have different areas and perimeters. Since every shape is measured differently, every formula for area and perimeter is different.

## Area

Defining an area means determining how much space there is within the perimeter of a 2D shape. The unit of measure is the square unit, such as cm^{2}, m^{2}, etc. When you need to find the area of a square formula, or any other quadrilateral, you need to multiply the length by the width. This means that, for instance, a rectangle with 3 cm and 4 cm sides would have an area of 12 cm^{2}.

## Solved Example

**Ques. Find the area of the square whose side is 11 cm.**

**Ans.** Since, Area of the square = (side)^{2}

Therefore, Area = (11)^{2}

= 11 x 11

Area = 121 cm^{2}

## Perimeter

Perimeters can be described as paths or boundaries surrounding a shape in geometry. The outline of a shape can also be thought of as its length. In two-dimensional shapes, the perimeter is the length of the sides. In order to determine the perimeter, the sides and edges of the shape are added together. As such, the perimeter is measured in units of length as well. The distance can thus be calculated in meters, kilometers, centimeters, etc. As well as inches, feet, and yards, miles are also accepted units of perimeter measurement.

Formula: Perimeter = Sum of all the sides.

## Solved Example

**Ques. Find the perimeter of a rectangle whose length and width are 8 cm and 12 cm, respectively.**

**Ans.** According to the question length (l) = 8cm and width (b) = 12cm

As, Perimeter of a rectangle = 2(l+b)

Hence, Perimeter = 2 ( 8+ 12)

= 2 ( 20)

We get, Perimeter = 40 cm.