Question

In the below fig. 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: 

(i) XY = 50 cm 

(ii) DCYX is a trapezium 

(iii) ar (trap. DCYX) = 9/11 ar (trap. (XYBA))

Answer 1

(i) Join DY and produce it to meet AB produced at P

(ii) We have

XY || AP

(iii) Since x and y are the midpoint of DA and CB respectively 

Trapezium DCXY and ABYX are of the same height say hm 

Now