The area of the rectangle in the diagram below is 15 cm2.
Giving reasons, find the area of the trapezium `ABCD`. (4 marks)
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`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`