Question

In the given figure, ABCD is a trapezium. P and Q are the midpoints of non-parallel side AD and BC respectively. Find: PQ, if AB = 12 cm and DC = 10 cm.

Answer 1

Let us draw a diagonal AC which meets PQ at O as shown below:

Given AB = 12 cm and DC = 10 cm
In ΔABC,

OQ = `(1)/(2)"AB"`      ....(Mid-point Theorem)

⇒ OQ = `(1)/(2) xx 12` = 6 cm

In ΔADC,

OP = `(1)/(2)"DC"`      ....(Mid-point Theorem)

⇒ OP = `(1)/(2) xx 10` = 5 cm
Now,
PQ = OP + OQ 
= 6 + 5
= 11 cm.