In a trapezium ABCD, AB and CD are parallel sides of length 10 cm and 15 cm respectively. Calculate the length of the line joining the mid-points of two non-parallel sides.

12.5 cm

Reason

Let E and F be midpoints of AD and BC, respectively.

Join diagonal BD.

In a trapezium, line joining midpoints of non-parallel sides is parallel to the parallel sides,

∴ AB || EF || DC

In Δ ABD, E is mid point of AD and EO || AB. By mid-point theorem,

EO = $\dfrac{1}{2}$AB …………….(1)

In Δ BDC, F is mid point of BC and OF || DC. By mid-point theorem,

OF = $\dfrac{1}{2}$DC …………….(2)

From the figure,

EF = EO + OF

= $\dfrac{1}{2}$AB + $\dfrac{1}{2}$DC

= $\dfrac{1}{2}$(AB + DC)

= $\dfrac{10 + 15}{2}$ cm

= $\dfrac{25}{2}$ cm

= 12.5 cm