Question

ABCD is a trapezium in which AB||CD and CD=40 cm and AB=60cm if X and Y are respectively the midpoint of AD and BC prove that i) XY =50cm ii) Area (trap. DCYX) =9/11 Area(trap XYBA)​

Answer 1

Step-by-step explanation:

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)

hope it will help u