## 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

1. Perimeter of the rectangle: p = 2(l + b) units.
1. Diagonal of the rectangle: d = √(l2 + b2) units.
2. Area of the rectangle : a = (l×b)sq. units.
3. Length = ( Area / Breadth ) units.
4. 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
1. Area of four walls = [2(l + b)×h] sq. units.
2. Diagonal of the room = √(l2 + b2 + h2) units.

## Square

### Perimeter and area of a square

1. Perimeter of the square: p = (4s) units.
2. Diagonal of the square: d = √(s2 + s2) units = √2s2 units = s√2 units.
3. Area of the square : a = s2 sq. units.
4. Area of the square : a = (1/2)d2 sq. units.
5. 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

1. Perimeter of the triangle: p = (a + b + c) units.
s = (a + b + c)/2 is called the semi-perimeter of the triangle.
2. Perimeter of an equilateral triangle: p = (3a) units.
3. Area of the triangle : Area = √(s(s-a)(s-b)(s-c)) sq. units.
4. Area of the triangle : Area = (1/2)bh sq. units.
5. Area of the equilateral triangle : Area = (√3/4)a2 sq. units.
6. 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

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