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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.
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Solution
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.
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