Measurements

Perimeter is the distance around and Area is the region occupied by the closed shape.

Parallelogram:-

A parallelogram is a four sided closed shape, in which opposite sides are both parallel and equal, the adjacent sides do not make right angles instead they make acute and obtuse angles.

Area and Perimeter of the Parallelogram:-

The area of the parallelogram is the same as that of the rectangle.

Area of the rectangle = length x breadth

= base x height sq. units.

= Area of the parallelogram.

Perimeter of a parallelogram is the sum of the lengths of the four sides.

Rhombus:-

In a rhombus,

· all the sides are equal

· opposite sides are parallel

· Diagonals divide the rhombus into 4 right angled triangles of equal area.

· the diagonals bisect each other at right angles

Area of the rhombus if base and height are given:

Area of the square = side × side sq.units

= base x height sq.units

= area of the rhombus

Area of the rhombus if the diagonals are given:

Here AB = BC = CD = DA and diagonals AC (d1) and BD (d2) are perpendicular to each other.

Area of the rhombus ABCD = Area of triangle ABC + Area of triangle ADC

= x AC x OB + x AC x OD

= x AC (OB+OD)

= x AC x BD

= x d1 × d2 sq. units

Area of the rhombus = (product of diagonals) square units

Trapezium:-

· A parallelogram with one pair of non-parallel sides is known as a Trapezium

· The distance between the parallel sides is the height of the trapezium.

Isosceles Trapezium :

If the non - parallel sides of a trapezium are equal (AB = CD) then, it is known as an isosceles trapezium.

Area of the Trapezium:-

ABCD is a trapezium with parallel sides AB and DC measuring ‘a ’units and ‘b’ units respectively. Let the distance between the two parallel sides be ‘h’ units. The diagonal BD divides the trapezium into two triangles ABD and BCD.

Area of the trapezium = x h (a+b) sq.units