Question

The parallel sides of a trapezium are x and y in length. The length of the line segement joining the mid points of the non parallel sides is

• A. $\frac{x+y}{2}$
• B. $x+y$
• C. $\frac{2x+3y}{2}$
• D. $\frac{xy}{2}$

Answer 1

The correct option is A $\frac{x+y}{2}$

Consider the given tapezium,

Area of trapezium $EFDC=(FE+x).\frac{h}{2}$ …..(1)

Area of trapezium $ABEF=\frac{1}{2}.(FE+y).\frac{h}{2}$ ….(2)

Area of trapezium,$ABCD=\frac{1}{2}.(x+y).h$ …..(3)

(1)+(2)=(3)

$\Rightarrow \frac{1}{2}.(FE+x).\frac{h}{2}+\frac{1}{2}(FE+y).\frac{h}{2}=\frac{1}{2}(x+y).h$

$\Rightarrow \frac{h}{2}.FE+\frac{1}{4}h.(x+y)=\frac{1}{2}(x+y)h$

$\Rightarrow \frac{h}{2}.FE=\frac{1}{4}.h(x+y)$

$\Rightarrow FE=\frac{x+y}{2}$

Hence, this is the answer.