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CBSE Class 9 Answered

ABCD is a trapezium In which AB  DC and DC = 40 cm and AB = 60 cm. If X and Y are respectively, the mid points of AD and BC, prove that ar (DCYX) = ar (XYBA).
Asked by Topperlearning User | 17 Aug, 2017, 02:01: PM
answered-by-expert Expert Answer
Since X and Y are the mid points of AD and BC respectively,
Trapezium DCYX and ABYX are of the same height, say h cm.
Area of trapezium DCYX = size 12px 1 over size 12px 2(DC + XY)h
                                          = size 12px 1 over size 12px 2(40 + 50) h 
                                          = 45 h cm2
XY = size 12px 1 over size 12px 2(AB + DC) = 50 cm.
Area of trapezium ABYX = size 12px 1 over size 12px 2(AB + XY) h
                                         = size 12px 1 over size 12px 2(60 + 50) h
                                         = 55 h cm2                                    
                                               
 ar (DCYX) = size 12px 9 over size 12px 11ar (ABYX)
Answered by | 17 Aug, 2017, 04:01: PM

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