### Area and Perimeter

Here we will learn about how to find area and perimeter of a plane figures. The perimeter is used to measure the boundaries and the area is used to measure the regions enclosed.

Perimeter:

The length of the boundary of a closed figure is called the perimeter of the plane figure. The units of perimeter are same as that of length, i.e., m, cm, mm, etc.

Area:

A part of the plane enclosed by a simple closed figure is called a plane region and the measurement of plane region enclosed is called its area.

Area is measured in square units.

The units of area and the relation between them is given below:

The different geometrical shapes formula of area and perimeter with examples are discussed below:

Perimeter and Area of Rectangle:

● The perimeter of rectangle = 2(l + b).

● Area of rectangle = l × b; (l and b are the length and breadth of rectangle)

● Diagonal of rectangle = √(l² + b²)

Perimeter and Area of the Square:

● Perimeter of square = 4 × S.

● Area of square = S × S.

● Diagonal of square = S√2; (S is the side of square)

Perimeter and Area of the Triangle:

● Perimeter of triangle = (a + b + c); (a, b, c are 3 sides of a triangle)

● Area of triangle = √(s(s – a) (s – b) (s – c)); (s is the semi-perimeter of triangle)

● S = 1/2 (a + b + c)

● Area of triangle = 1/2 × b × h; (b base , h height)

● Area of an equilateral triangle = (a²√3)/4; (a is the side of triangle)

Perimeter and Area of the Parallelogram:

● Perimeter of parallelogram = 2 (sum of adjacent sides)

● Area of parallelogram = base × height

Perimeter and Area of the Rhombus:

● Area of rhombus = base × height

● Area of rhombus = 1/2 × length of one diagonal × length of other diagonal

● Perimeter of rhombus = 4 × side

Perimeter and Area of the Trapezium:

● Area of trapezium = 1/2 (sum of parallel sides) × (perpendicular distance between them)
= 1/2 (p₁ + p₂) × h (p₁, p₂ are 2 parallel sides)

Circumference and Area of Circle:

● Circumference of circle = 2πr
= πd
Where, π = 3.14 or π = 22/7
r is the radius of circle
d is the diameter of circle
● Area of circle = πr²

● Area of ring = Area of outer circle – Area of inner circle.