Plane Figures


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

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

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

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

Trapezium

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





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