Question

Is trapezium having different parameter has same area? Prove with the help of the data given in the following figures.

Answer 1

(i) Perimeter of Trapezium = 4 + 9 + 8 + 9 = 30 units

PT is parallel to QR and PU ⊥ RS

∵ PT || QR and PQ || TR

∴ PQRT is a parallelogram.

∴ PT = QR = 9 unit and TR = PQ = 4 unit

∴ ST = RS – RT = 8 – 4 = 4 unit

(ii) Perimeter of trapezium (ii)

= 7 + 6 + 6 + 10 = 29 units

From (i), (ii) and (iii) it is clear that trapezium having different perimeters can not have same area.