## Perimeter of a plane figure

**The length of the boundary enclosing the plane figure is called the perimeter of the plane figure.** ** **

## Area of a plane figure

**The amount of surface enclosed by the boundary of the plane figure is called the area of the plane figure.**

## Rectangle

### Perimeter and area of a rectangle

- Perimeter of the rectangle: p = 2(l + b) units.

- Diagonal of the rectangle: d = √(l
^{2} + b^{2}) units.
- Area of the rectangle : a = (l×b)sq. units.
- Length = ( Area / Breadth ) units.
- Breadth = ( Area / Length ) units.

### Area of four walls of a room

There is a room of length = l units, width = b units and height = h units. Then

- Area of four walls = [2(l + b)×h] sq. units.
- Diagonal of the room = √(l
^{2} + b^{2} + h^{2}) units.

## Square

### Perimeter and area of a square

- Perimeter of the square: p = (4s) units.
- Diagonal of the square: d = √(s
^{2} + s^{2}) units = √2s^{2} units = s√2 units.
- Area of the square : a = s
^{2} sq. units.
- Area of the square : a = (1/2)d
^{2} sq. units.
- Side of the square = √a units.

Square is a special case of rectangle when all the sides have same length.

## Triangle

### Perimeter and area of a Triangle

- Perimeter of the triangle: p = (a + b + c) units.

s = (a + b + c)/2 is called the semi-perimeter of the triangle.
- Perimeter of an equilateral triangle: p = (3a) units.
- Area of the triangle : Area = √(s(s-a)(s-b)(s-c)) sq. units.
- Area of the triangle : Area = (1/2)bh sq. units.
- Area of the equilateral triangle : Area = (√3/4)a
^{2} sq. units.
- Height of the equilateral triangle of side a = (√3/2)a units.

A right triangle is a triangle with one angle as right angle.

## Trapezium

### Area of a trapezium

- Area of the trapezium : Area = (1/2)×(sum of parallel sides)×(distance between them)
- Area of the trapezium : Area = (1/2)×(a+b)×(h) sq. units