At what horizontal distance from A should a vertical line be drawn so as to divide the area of the trapezium shown in the figure into two equal parts ? (a and b are lengths of the parallel sides.)

Correct option is A

Solution:
Let the vertical line be drawn at a distance x from A.
EA = x = FDE
BE = a−x
CF = b−x

The area of trapezium EBCF equals the area of trapezium AEFD:
Area formula: (1/2) × EF × ((a - x) + (b - x)) = EF × x
Simplify the equation: (1/2) × EF × (a + b - 2x) = EF × x
a + b - 2x = 2x
4x = a + b
Solve for x: x = (a + b) / 4
Final Answer: The vertical line should be drawn at a distance (a + b) / 4 from A.