Class 09 To find the formula for the area of atrapezium experimentally.

 Activity 25 

OBJECTIVE	MATERIAL REQUIRED
To find the formula for the area of a	Hardboard, thermocol, coloured
trapezium experimentally.	glazed papers, adhesive, scissors.

 METHOD OF CONSTRUCTION

 1.   Take a piece of hardboard for the base of the model.

 2.   Cut two congruent trapeziums of parallel sides a and b units [see Fig. 1].

 Place them on the hardboard as shown in Fig. 2

DEMONSTRATION

 1.    Figure formed by the two trapeziums [see Fig. 2] is a parallelogram ABCD.

 2.   Side AB of the parallelogram = (a + b) units and its corresponding altitude = h units. 

3. Area of each trapezium	=	1	(area of parallelogram)	=	1	( a + b ) × h
	2			2

1Therefore, area of trapezium =     ( a + b)× h 

1= ₂ (sum of parallel sides) × perpendicular distance.

 Here, area is in square units.

 -------------------

OBSERVATION
Lengths of parallel sides of the trapezium =			-------,-------.
Length of altitude of the parallelogram = --------			.
Area of parallelogram = ---------------		.
Area of the trapezium =	1	(Sum of	sides) ×	.
2

 APPLICATION

 This concept is used for finding the formula for area of a triangle in coordinate geometry. This may also be used in finding the area of a field which can be split into different trapeziums and right triangles.