Congruence, SMB-014 The area of the rectangle in the diagram below is 15 cm2. Giving reasons, find the area of the trapezium `ABCD`. (4 marks) --- 8 WORK AREA LINES (style=lined) --- Show Answers Only `30\ text(cm)^2` Show Worked Solution `text{Opposite sides of rectangles are equal and parallel}` `\Delta AEI ≡ \Delta DHJ\ \ text{(RHS)}` `/_ EAI = /_ BEF\ \ text{(corresponding,}\ AD\ text{||}\ EH )` `\Delta AEI ≡ \Delta EBF\ \ text{(AAS)}` `text{Similarly,}\ \Delta DHJ ≡ \Delta HCG\ \ text{(AAS)}` `=>\ \text{All triangles in diagram are congruent.}` `text(Rearranging the diagram:)` `:.\ text(Area of trapezium)` `= 2 xx 15` `= 30\ text(cm)^2`