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

Objective

To find the formula for the area of a trapezium experimentally.

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.
    Lab Manual: Find the Formula for the Area of a Trapezium | Lab Manuals for Class 9Area 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)
    Lab Manual: Find the Formula for the Area of a Trapezium | Lab Manuals for Class 9
  • Now, place both trapeziums on cardboard, (see Fig. below)
    Lab Manual: Find the Formula for the Area of a Trapezium | Lab Manuals for Class 9

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.
The document Lab Manual: Find the Formula for the Area of a Trapezium | Lab Manuals for Class 9 is a part of the Class 9 Course Lab Manuals for Class 9.
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