Lab Manual: Find the Formula for the Area of a Trapezium - Class 9 PDF Download

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Objective

Materials Required
Cardboard, Thermocol, Geometry box, Drawing sheets, Scissors, Adhesive

Prerequisite Knowledge

• Concept of a trapezium.
• Area of a parallelogram.

Theory

• A quadrilateral in which one pair of opposite sides are parallel and one pair of opposite sides are non-parallel, is called a trapezium. In Fig. below, ABCD is a trapezium, in which AB||CD and AD, BC are non-parallel.
  Area of trapezium = ½ (Sum of parallel sides) x Distance between parallel sides (Altitude)
  = ½(AB + CD) x DE
  If two non-parallel sides of a trapezium are equal, then it is called an isosceles trapezium.
• Area of parallelogram = Base x Height
  • Parallelograms on the same base and between the same parallels are equal in area.
  • If a triangle and a parallelogram are on the same base and between the same parallels, then the area of the triangle is equal to half the area of the parallelogram.

Procedure

• Take a cardboard piece of suitable size and by using adhesive, paste a drawing sheet on it.
• By using thermocol sheet, cut out two congruent trapeziums of parallel sides x and y units with h units altitude.(see Fig. below)
  

• Now, place both trapeziums on cardboard, (see Fig. below)
  

Demonstration

• In Fig. above, figure formed by placing, both trapeziums together is a parallelogram.
• Base of parallelogram = (x + y) units and corresponding altitude = h units
• Now, Area of trapezium = ½ (Area of parallelogram)
  = ½ (Base of parallelogram x Corresponding altitude)
  = ½[(x + y) x h]
  Hence, area of trapezium = ½ x (x + y) x h .
  = ½ x (Sum of parallel sides) x Altitude Here, area is in square units.

Observation
Lengths of parallel sides of the trapezium = ………….. , ……………
Length of altitude of the parallelogram = ……………
Area of the parallelogram = ……………
Area of the trapezium = ½ (Sum of …… sides) x ………….

Result
We have verified experimentally the formula for the area of a trapezium.

Application
This concept is used in

• finding the formula for area of a triangle, in coordinate geometry.
• deriving the area of a field which can be split into different trapeziums and right triangles.