Question

observation on :

To verify the formula for area of a trapezium? ​

Answer 1

Answer:

Step-by-step explanation:

A trapezium is a quadrilateral having one pair of parallel opposite sides. In the given figure, ABCD is a trapezium in which AB ∥ DC.

Area of a Trapezium:

Let ABCD be a trapezium in which AB ∥ DC, CE ⊥ AB, DF ⊥ AB and CE = DF = h.

Prove that:

Area of a trapezium ABCD = {¹/₂ × (AB + DC) × h} square units.

Proof:     Area of a trapezium ABCD

           = area (∆DFA) + area (rectangle DFEC) + area (∆CEB)

           = (¹/₂ × AF × DF) + (FE × DF) + (¹/₂ × EB × CE)

          = (¹/₂ × AF × h) + (FE × h) + (¹/₂ × EB × h)

           = ¹/₂ × h × (AF + 2FE + EB)

           = ¹/₂ × h × (AF + FE + EB + FE)

           = ¹/₂ × h × (AB + FE)

           = ¹/₂ × h × (AB + DC) square units.

           = ¹/₂ × (sum of parallel sides) × (distance between them)

Formula of Area of a trapezium = ¹/₂ × (sum of parallel sides) × (distance between them)

Answer 2

Answer:

It has been geometrically proved that the area of a trapezium is given by area = ½ x (sum of the parallel sides) x height. Step 1: Draw any trapezium ABCD in which AB || DC on a sheet of white paper as shown in Figure 30.1. Let AB = a units and DC = b units and the height of the trapezium = h units.